diff --git a/test/parameters_matrix.jl b/test/parameters_matrix.jl
index ae86e8c..5f2be86 100644
--- a/test/parameters_matrix.jl
+++ b/test/parameters_matrix.jl
@@ -62,7 +62,7 @@ using ParameterHandling: vec_to_tril, tril_to_vec
         X.L .= 0 # zero the unconstrained value
         @test isposdef(value(X))
         @test X != positive_definite(X_mat)
-        @test positive_definite(X_mat, 1e-3) != positive_definite(X_mat, 1e-2)
+        @test positive_definite(X_mat, 1e-5) != positive_definite(X_mat, 1e-6)
         @test_throws ArgumentError positive_definite(zeros(3, 3))
         @test_throws ArgumentError positive_definite(X_mat, 0.0)
         test_parameter_interface(X)