diff --git a/pytorch3d/transforms/rotation_conversions.py b/pytorch3d/transforms/rotation_conversions.py
index b5f73bf5..459441ca 100644
--- a/pytorch3d/transforms/rotation_conversions.py
+++ b/pytorch3d/transforms/rotation_conversions.py
@@ -155,10 +155,10 @@ def matrix_to_quaternion(matrix: torch.Tensor) -> torch.Tensor:
 
     # if not for numerical problems, quat_candidates[i] should be same (up to a sign),
     # forall i; we pick the best-conditioned one (with the largest denominator)
-
-    return quat_candidates[
+    out = quat_candidates[
         F.one_hot(q_abs.argmax(dim=-1), num_classes=4) > 0.5, :
     ].reshape(batch_dim + (4,))
+    return standardize_quaternion(out)
 
 
 def _axis_angle_rotation(axis: str, angle: torch.Tensor) -> torch.Tensor: