diff --git a/src/linalg/cholesky.rs b/src/linalg/cholesky.rs
index 4d667fbc1..bf7d8e8f8 100644
--- a/src/linalg/cholesky.rs
+++ b/src/linalg/cholesky.rs
@@ -235,10 +235,16 @@ where
             }
 
             let sqrt_denom = |v: T| {
-                if v.is_zero() {
+                // positive definiteness requires the diagonal to be real and strictly positive
+                if !v.clone().imaginary().is_zero() {
                     return None;
                 }
-                v.try_sqrt()
+                let re = v.real();
+                if re <= T::RealField::zero() {
+                    return None;
+                }
+                // fixme: could be improved by sqrt on real, e.g. `T::from_real(re.sqrt())`
+                Some(T::from_real(re).sqrt())
             };
 
             let diag = unsafe { matrix.get_unchecked((j, j)).clone() };
diff --git a/tests/linalg/cholesky.rs b/tests/linalg/cholesky.rs
index bd135fb6a..d0ee92b9a 100644
--- a/tests/linalg/cholesky.rs
+++ b/tests/linalg/cholesky.rs
@@ -11,6 +11,20 @@ fn cholesky_with_substitute() {
     assert!(na::Cholesky::new_with_substitute(m, 1e-8).is_some());
 }
 
+// 2x2 matrix filled with -1 is not positive definite and should not return a Cholesky
+// decomposition (regardless of element type).
+// See https://github.com/dimforge/nalgebra/issues/1536 .
+#[test]
+fn cholesky_check_positive_definiteness() {
+    let x = -1.0;
+    let m = na::Matrix2::new(x, x, x, x);
+    assert!(nalgebra::Cholesky::new(m).is_none());
+
+    let x = na::Complex::new(-1.0, 0.0);
+    let m = na::Matrix2::new(x, x, x, x);
+    assert!(nalgebra::Cholesky::new(m).is_none());
+}
+
 macro_rules! gen_tests(
     ($module: ident, $scalar: ty) => {
         mod $module {