diff --git a/smt/surrogate_models/krg_based.py b/smt/surrogate_models/krg_based.py
index f06443827..0011034d3 100644
--- a/smt/surrogate_models/krg_based.py
+++ b/smt/surrogate_models/krg_based.py
@@ -1667,6 +1667,8 @@ def _predict_variances(self, x: np.ndarray, is_acting=None) -> np.ndarray:
         )
         A = self.optimal_par["sigma2"]
         B = 1.0 - (rt**2.0).sum(axis=0) + (u**2.0).sum(axis=0)
+        # machine precision: force to zero!
+        B[B<1e-12]=0
         MSE = np.einsum("i,j -> ji", A, B)
         # Mean Squared Error might be slightly negative depending on
         # machine precision: force to zero!