diff --git a/native/dorgtr.go b/native/dorgtr.go
new file mode 100644
index 00000000..5a1cf714
--- /dev/null
+++ b/native/dorgtr.go
@@ -0,0 +1,89 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package native
+
+import "github.com/gonum/blas"
+
+// Dorgtr generates a real orthogonal matrix Q which is defined as the product
+// of n-1 elementary reflectors of order n as returned by Dsytrd.
+//
+// The construction of Q depends on the value of uplo:
+//  Q = H[n-1] * ... * H[1] * H[0]  if uplo == blas.Upper
+//  Q = H[0] * ... * H[n-1]         if uplo == blas.Lower
+// where H[i] is constructed from the elementary reflectors as computed by Dsytrd.
+// See the documentation for Dsytrd for more information.
+//
+// tau must have length at least n-1, and Dorgtr will panic otherwise.
+//
+// work is temporary storage, and lwork specifies the usable memory length. At
+// minimum, lwork >= n-1, and Dorgtr will panic otherwise. The amount of blocking
+// is limited by the usable length.
+// If lwork == -1, instead of computing Dorgtr the optimal work length is stored
+// into work[0].
+func (impl Implementation) Dorgtr(uplo blas.Uplo, n int, a []float64, lda int, tau, work []float64, lwork int) {
+	checkMatrix(n, n, a, lda)
+	if len(tau) < n-1 {
+		panic(badTau)
+	}
+	upper := uplo == blas.Upper
+	var nb int
+	if upper {
+		nb = impl.Ilaenv(1, "DORGQL", " ", n-1, n-1, n-1, -1)
+	} else {
+		nb = impl.Ilaenv(1, "DORGQR", " ", n-1, n-1, n-1, -1)
+	}
+	lworkopt := max(1, n-1) * nb
+	work[0] = float64(lworkopt)
+	if lwork == -1 {
+		return
+	}
+	if len(work) < lwork {
+		panic(badWork)
+	}
+	if lwork < n-1 {
+		panic(badWork)
+	}
+	if n == 0 {
+		return
+	}
+	if upper {
+		// Q was determined by a call to Dsytrd with uplo == blas.Upper.
+		// Shift the vectors which define the elementary reflectors one column
+		// to the left, and set the last row and column of Q to those of the unit
+		// matrix.
+		for j := 0; j < n-1; j++ {
+			for i := 0; i < j; i++ {
+				a[i*lda+j] = a[i*lda+j+1]
+			}
+			a[(n-1)*lda+j] = 0
+		}
+		for i := 0; i < n-1; i++ {
+			a[i*lda+n-1] = 0
+		}
+		a[(n-1)*lda+n-1] = 1
+
+		// Generate Q[0:n-1, 0:n-1].
+		impl.Dorgql(n-1, n-1, n-1, a, lda, tau, work, lwork)
+	} else {
+		// Q was determined by a call to Dsytrd with uplo == blas.Upper.
+		// Shift the vectors which define the elementary reflectors one column
+		// to the right, and set the first row and column of Q to those of the unit
+		// matrix.
+		for j := n - 1; j > 0; j-- {
+			a[j] = 0
+			for i := j + 1; i < n; i++ {
+				a[i*lda+j] = a[i*lda+j-1]
+			}
+		}
+		a[0] = 1
+		for i := 1; i < n; i++ {
+			a[i*lda] = 0
+		}
+		if n > 1 {
+			// Generate Q[1:n, 1:n].
+			impl.Dorgqr(n-1, n-1, n-1, a[lda+1:], lda, tau, work, lwork)
+		}
+	}
+}
diff --git a/native/dsytrd.go b/native/dsytrd.go
index fc3399bf..f901a94f 100644
--- a/native/dsytrd.go
+++ b/native/dsytrd.go
@@ -135,7 +135,7 @@ func (impl Implementation) Dsytrd(uplo blas.Uplo, n int, a []float64, lda int, d
 			// Update the unreduced submatrix A[i+ib:n, i+ib:n], using an update
 			// of the form A = A + V*W^T - W*V^T.
 			bi.Dsyr2k(uplo, blas.NoTrans, n-i-nb, nb, -1, a[(i+nb)*lda+i:], lda,
-				work[nb+i:], ldwork, 1, a[(i+nb)*lda+i+nb:], lda)
+				work[nb*ldwork:], ldwork, 1, a[(i+nb)*lda+i+nb:], lda)
 
 			// Copy subdiagonal elements back into A, and diagonal elements into D.
 			for j := i; j < i+nb; j++ {
diff --git a/native/lapack_test.go b/native/lapack_test.go
index 0e7cddb6..1f535f65 100644
--- a/native/lapack_test.go
+++ b/native/lapack_test.go
@@ -188,6 +188,10 @@ func TestDorgqr(t *testing.T) {
 	testlapack.DorgqrTest(t, impl)
 }
 
+func TestDorgtr(t *testing.T) {
+	testlapack.DorgtrTest(t, impl)
+}
+
 func TestDormbr(t *testing.T) {
 	testlapack.DormbrTest(t, impl)
 }
diff --git a/testlapack/dorgqr.go b/testlapack/dorgqr.go
index 99862770..a2c30036 100644
--- a/testlapack/dorgqr.go
+++ b/testlapack/dorgqr.go
@@ -23,7 +23,7 @@ func DorgqrTest(t *testing.T, impl Dorgqrer) {
 		{10, 10, 10, 0},
 		{10, 10, 10, 20},
 		{30, 10, 10, 0},
-		{30, 20, 10, 0},
+		{30, 20, 10, 20},
 
 		{100, 100, 100, 0},
 		{100, 100, 50, 0},
diff --git a/testlapack/dorgtr.go b/testlapack/dorgtr.go
new file mode 100644
index 00000000..7f1e815d
--- /dev/null
+++ b/testlapack/dorgtr.go
@@ -0,0 +1,117 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+	"github.com/gonum/floats"
+)
+
+type Dorgtrer interface {
+	Dorgtr(uplo blas.Uplo, n int, a []float64, lda int, tau, work []float64, lwork int)
+	Dsytrder
+}
+
+func DorgtrTest(t *testing.T, impl Dorgtrer) {
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, test := range []struct {
+			n, lda int
+		}{
+			{6, 0},
+			{33, 0},
+			{100, 0},
+
+			{6, 10},
+			{33, 50},
+			{100, 120},
+		} {
+			n := test.n
+			lda := test.lda
+			if lda == 0 {
+				lda = n
+			}
+			a := make([]float64, n*lda)
+			for i := range a {
+				a[i] = rand.NormFloat64()
+			}
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+
+			d := make([]float64, n)
+			e := make([]float64, n-1)
+			tau := make([]float64, n-1)
+			work := make([]float64, 1)
+			impl.Dsytrd(uplo, n, a, lda, d, e, tau, work, -1)
+			work = make([]float64, int(work[0]))
+			impl.Dsytrd(uplo, n, a, lda, d, e, tau, work, len(work))
+
+			impl.Dorgtr(uplo, n, a, lda, tau, work, -1)
+			work = make([]float64, int(work[0]))
+			for i := range work {
+				work[i] = math.NaN()
+			}
+			impl.Dorgtr(uplo, n, a, lda, tau, work, len(work))
+
+			q := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: lda,
+				Data:   a,
+			}
+			tri := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, n*n),
+			}
+			for i := 0; i < n; i++ {
+				tri.Data[i*tri.Stride+i] = d[i]
+				if i != n-1 {
+					tri.Data[i*tri.Stride+i+1] = e[i]
+					tri.Data[(i+1)*tri.Stride+i] = e[i]
+				}
+			}
+
+			aMat := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, n*n),
+			}
+			if uplo == blas.Upper {
+				for i := 0; i < n; i++ {
+					for j := i; j < n; j++ {
+						v := aCopy[i*lda+j]
+						aMat.Data[i*aMat.Stride+j] = v
+						aMat.Data[j*aMat.Stride+i] = v
+					}
+				}
+			} else {
+				for i := 0; i < n; i++ {
+					for j := 0; j <= i; j++ {
+						v := aCopy[i*lda+j]
+						aMat.Data[i*aMat.Stride+j] = v
+						aMat.Data[j*aMat.Stride+i] = v
+					}
+				}
+			}
+
+			tmp := blas64.General{Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n)}
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, q, 0, tmp)
+
+			ans := blas64.General{Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n)}
+			blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tmp, 0, ans)
+
+			if !floats.EqualApprox(ans.Data, tri.Data, 1e-8) {
+				t.Errorf("Recombination mismatch. n = %v, isUpper = %v", n, uplo == blas.Upper)
+			}
+		}
+	}
+}