diff --git a/nibabel/nifti1.py b/nibabel/nifti1.py
index 9bb88e844..8502ad4fa 100644
--- a/nibabel/nifti1.py
+++ b/nibabel/nifti1.py
@@ -1098,7 +1098,10 @@ def set_qform(self, affine, code=None, strip_shears=True):
         # (a subtle requirement of the NIFTI format qform transform)
         # Transform below is polar decomposition, returning the closest
         # orthogonal matrix PR, to input R
-        P, S, Qs = npl.svd(R)
+        try:
+            P, S, Qs = npl.svd(R)
+        except np.linalg.LinAlgError as e:
+            raise HeaderDataError(f'Could not decompose affine:\n{affine}') from e
         PR = np.dot(P, Qs)
         if not strip_shears and not np.allclose(PR, R):
             raise HeaderDataError('Shears in affine and `strip_shears` is False')