diff --git a/gtsam/geometry/Rot2.cpp b/gtsam/geometry/Rot2.cpp
index d43b9b12d..9bf631e50 100644
--- a/gtsam/geometry/Rot2.cpp
+++ b/gtsam/geometry/Rot2.cpp
@@ -131,11 +131,14 @@ Rot2 Rot2::relativeBearing(const Point2& d, OptionalJacobian<1, 2> H) {
 
 /* ************************************************************************* */
 Rot2 Rot2::ClosestTo(const Matrix2& M) {
-  double c = M(0, 0);
-  double s = M(1, 0);
-  double theta_rad = std::atan2(s, c);
-  c = cos(theta_rad);
-  s = sin(theta_rad);
+  Eigen::JacobiSVD<Matrix2> svd(M, Eigen::ComputeFullU | Eigen::ComputeFullV);
+  const Matrix2& U = svd.matrixU();
+  const Matrix2& V = svd.matrixV();
+  const double det = (U * V.transpose()).determinant();
+  Matrix2 M_prime = (U * Vector2(1, det).asDiagonal() * V.transpose());
+
+  double c = M_prime(0, 0);
+  double s = M_prime(1, 0);
   return Rot2::fromCosSin(c, s);
 }