diff --git a/pyerrors/fits.py b/pyerrors/fits.py
index 6db0b1dc..17da5e71 100644
--- a/pyerrors/fits.py
+++ b/pyerrors/fits.py
@@ -464,8 +464,10 @@ def _standard_fit(x, y, func, silent=False, **kwargs):
         corr = covariance(y, correlation=True)
         covdiag = np.diag(1 / np.asarray(dy_f))
         condn = np.linalg.cond(corr)
-        if condn > 1e8:
-            warnings.warn("Correlation matrix may be ill-conditioned, condition number: %1.2e" % (condn), RuntimeWarning)
+        if condn > 0.1 / np.finfo(float).eps:
+            raise Exception(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
+        if condn > 1 / np.sqrt(np.finfo(float).eps):
+            warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
         chol = np.linalg.cholesky(corr)
         chol_inv = np.linalg.inv(chol)
         chol_inv = np.dot(chol_inv, covdiag)
diff --git a/tests/fits_test.py b/tests/fits_test.py
index cc958dbc..b6236fb9 100644
--- a/tests/fits_test.py
+++ b/tests/fits_test.py
@@ -375,6 +375,12 @@ def test_fit_no_autograd():
         pe.total_least_squares(oy, oy, func)
 
 
+def test_singular_correlated_fit():
+    obs1 = pe.pseudo_Obs(1.0, 0.1, 'test')
+    with pytest.raises(Exception):
+        pe.fits.fit_lin([0, 1], [obs1, obs1], correlated_fit=True)
+
+
 def test_ks_test():
     def f(a, x):
         y = a[0] + a[1] * x