diff --git a/tests/fits_test.py b/tests/fits_test.py
index b6236fb9..374550e4 100644
--- a/tests/fits_test.py
+++ b/tests/fits_test.py
@@ -157,6 +157,28 @@ def test_correlated_fit():
             assert(diff.is_zero_within_error(sigma=5))
 
 
+def test_fit_corr_independent():
+    dim = 50
+    x = np.arange(dim)
+    y = 0.84 * np.exp(-0.12 * x) + np.random.normal(0.0, 0.1, dim)
+    yerr = [0.1] * dim
+
+    oy = []
+    for i, item in enumerate(x):
+        oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))
+
+    def func(a, x):
+        y = a[0] * anp.exp(-a[1] * x)
+        return y
+
+    out = pe.least_squares(x, oy, func)
+    out_corr = pe.least_squares(x, oy, func, correlated_fit=True)
+
+    assert np.isclose(out.chisquare, out_corr.chisquare)
+    assert (out[0] - out_corr[0]).is_zero(atol=1e-5)
+    assert (out[1] - out_corr[1]).is_zero(atol=1e-5)
+
+
 def test_total_least_squares():
     dim = 10 + int(30 * np.random.rand())
     x = np.arange(dim) + np.random.normal(0.0, 0.15, dim)