diff --git a/doc/whatsnew.rst b/doc/whatsnew.rst
index d78d23a3..e7f117a1 100644
--- a/doc/whatsnew.rst
+++ b/doc/whatsnew.rst
@@ -25,6 +25,7 @@ Bug fixes/enhancements:
 - fixed function definition for ``StepModel(form='linear')``, was not consistent with the other ones. (@matpompili; PR #794)
 - fixed height factor for ``Gaussian2dModel``, was not correct. (@matpompili; PR #795)
 - added ``Pearson4`` fitting model
+- for covariances with negative diagonal elements, we set the covariance to ``None`` (PR #813)
 
 Deprecations:
 
diff --git a/lmfit/minimizer.py b/lmfit/minimizer.py
index fd7b0f8c..e9c3c0b7 100644
--- a/lmfit/minimizer.py
+++ b/lmfit/minimizer.py
@@ -788,8 +788,12 @@ def _calculate_covariance_matrix(self, fvars):
             Hfun = ndt.Hessian(self.penalty, step=1.e-4)
             hessian_ndt = Hfun(fvars)
             cov_x = inv(hessian_ndt) * 2.0
+
+            if cov_x.diagonal().min() < 0:
+                # we know the calculated covariance is incorrect, so we set the covariance to None
+                cov_x = None
         except (LinAlgError, ValueError):
-            return None
+            cov_x = None
         finally:
             self.result.nfev = nfev