diff --git a/gtsam/geometry/Unit3.cpp b/gtsam/geometry/Unit3.cpp
index db4c8da83..ad6a41bde 100644
--- a/gtsam/geometry/Unit3.cpp
+++ b/gtsam/geometry/Unit3.cpp
@@ -58,7 +58,7 @@ Unit3 Unit3::Random(boost::mt19937 & rng) {
 }
 
 /* ************************************************************************* */
-Matrix Unit3::basis() const {
+const Matrix& Unit3::basis() const {
 
   // Return cached version if exists
   if (B_.rows() == 3)
diff --git a/gtsam/geometry/Unit3.h b/gtsam/geometry/Unit3.h
index 39e2c9799..8d2c024c0 100644
--- a/gtsam/geometry/Unit3.h
+++ b/gtsam/geometry/Unit3.h
@@ -84,7 +84,7 @@ public:
    * It is a 3*2 matrix [b1 b2] composed of two orthogonal directions
    * tangent to the sphere at the current direction.
    */
-  Matrix basis() const;
+  const Matrix& basis() const;
 
   /// Return skew-symmetric associated with 3D point on unit sphere
   Matrix skew() const;