diff --git a/src/structure.rs b/src/structure.rs
index abcd450..8721e51 100644
--- a/src/structure.rs
+++ b/src/structure.rs
@@ -603,6 +603,13 @@ where
         }
     }
 
+    /// Return the angle, normalized to the range `[-turn_div_2, turn_div_2)`.
+    #[inline]
+    fn normalize_signed(self) -> Self {
+        let rem = self.normalize();
+        if Self::turn_div_2() < rem { rem - Self::full_turn() } else { rem }
+    }
+
     /// Return the angle rotated by half a turn.
     #[inline]
     fn opposite(self) -> Self {
diff --git a/tests/angle.rs b/tests/angle.rs
index 309bd48..ddaeb52 100644
--- a/tests/angle.rs
+++ b/tests/angle.rs
@@ -17,7 +17,25 @@
 extern crate approx;
 extern crate cgmath;
 
-use cgmath::{Deg, Rad};
+use cgmath::{Angle, Deg, Rad};
+
+#[test]
+fn test_normalize_signed() {
+    let angle: Rad<f64> = Rad::full_turn().normalize_signed();
+    assert_ulps_eq!(&angle, &Rad(0f64));
+
+    let angle: Rad<f64> = (Rad::full_turn() + Rad::turn_div_4()).normalize_signed();
+    assert_ulps_eq!(&angle, &Rad::turn_div_4());
+
+    let angle: Rad<f64> = (Rad::full_turn() - Rad::turn_div_4()).normalize_signed();
+    assert_ulps_eq!(&angle, &-Rad::turn_div_4());
+
+    let angle: Rad<f64> = Rad::turn_div_2().normalize_signed();
+    assert_ulps_eq!(&angle, &Rad::turn_div_2());
+
+    let angle: Rad<f64> = (-Rad::turn_div_2()).normalize_signed();
+    assert_ulps_eq!(&angle, &Rad::turn_div_2());
+}
 
 #[test]
 fn test_conv() {