diff --git a/src/Math/Quaternion.h b/src/Math/Quaternion.h
index 4effe4f28..adaf3c5fa 100644
--- a/src/Math/Quaternion.h
+++ b/src/Math/Quaternion.h
@@ -20,6 +20,7 @@
  */
 
 #include <cmath>
+#include <Utility/Assert.h>
 #include <Utility/Debug.h>
 
 #include "Vector3.h"
@@ -134,13 +135,26 @@ template<class T> class Quaternion {
         /**
          * @brief Inverted quaternion
          *
-         * If the quaternion is already normalized, this function is
-         * equivalent to conjugated().
+         * See invertedNormalized() which is faster for normalized
+         * quaternions.
          */
         inline Quaternion<T> inverted() const {
             return conjugated()/lengthSquared();
         }
 
+        /**
+         * @brief Inverted normalized quaternion
+         *
+         * Equivalent to conjugated(). Assumes that the quaternion is
+         * normalized.
+         */
+        inline Quaternion<T> invertedNormalized() const {
+            CORRADE_ASSERT(MathTypeTraits<T>::equals(lengthSquared(), T(1)),
+                           "Math::Quaternion::invertedNormalized(): quaternion must be normalized",
+                           Quaternion({}, std::numeric_limits<T>::quiet_NaN()));
+            return conjugated();
+        }
+
     private:
         Vector3<T> _vector;
         T _scalar;
diff --git a/src/Math/Test/CMakeLists.txt b/src/Math/Test/CMakeLists.txt
index c193b8335..13b60f6ab 100644
--- a/src/Math/Test/CMakeLists.txt
+++ b/src/Math/Test/CMakeLists.txt
@@ -20,4 +20,4 @@ corrade_add_test(MathSwizzleTest SwizzleTest.cpp LIBRARIES MagnumMathTestLib)
 
 corrade_add_test(MathQuaternionTest MathQuaternionTest.cpp LIBRARIES MagnumMathTestLib)
 
-set_target_properties(MathVectorTest MathMatrix3Test MathMatrix4Test PROPERTIES COMPILE_FLAGS -DCORRADE_GRACEFUL_ASSERT)
+set_target_properties(MathVectorTest MathMatrix3Test MathMatrix4Test MathQuaternionTest PROPERTIES COMPILE_FLAGS -DCORRADE_GRACEFUL_ASSERT)
diff --git a/src/Math/Test/MathQuaternionTest.cpp b/src/Math/Test/MathQuaternionTest.cpp
index 24fccec56..0e3de5aa0 100644
--- a/src/Math/Test/MathQuaternionTest.cpp
+++ b/src/Math/Test/MathQuaternionTest.cpp
@@ -31,6 +31,7 @@ class QuaternionTest: public Corrade::TestSuite::Tester {
         void normalized();
         void conjugated();
         void inverted();
+        void invertedNormalized();
 
         void debug();
 };
@@ -46,6 +47,7 @@ QuaternionTest::QuaternionTest() {
              &QuaternionTest::normalized,
              &QuaternionTest::conjugated,
              &QuaternionTest::inverted,
+             &QuaternionTest::invertedNormalized,
              &QuaternionTest::debug);
 }
 
@@ -94,6 +96,23 @@ void QuaternionTest::inverted() {
     CORRADE_COMPARE(inverted, Quaternion({-1.0f, -3.0f, 2.0f}, -4.0f)/30.0f);
 }
 
+void QuaternionTest::invertedNormalized() {
+    Quaternion a = Quaternion({1.0f, 3.0f, -2.0f}, -4.0f);
+
+    std::ostringstream o;
+    Corrade::Utility::Error::setOutput(&o);
+    Quaternion notInverted = a.invertedNormalized();
+    CORRADE_COMPARE(notInverted.vector(), Vector3());
+    CORRADE_COMPARE(notInverted.scalar(), std::numeric_limits<float>::quiet_NaN());
+    CORRADE_COMPARE(o.str(), "Math::Quaternion::invertedNormalized(): quaternion must be normalized\n");
+
+    Quaternion aNormalized = a.normalized();
+    Quaternion inverted = aNormalized.invertedNormalized();
+    CORRADE_COMPARE(aNormalized*inverted, Quaternion());
+    CORRADE_COMPARE(inverted*aNormalized.normalized(), Quaternion());
+    CORRADE_COMPARE(inverted, Quaternion({-1.0f, -3.0f, 2.0f}, -4.0f)/std::sqrt(30.0f));
+}
+
 void QuaternionTest::debug() {
     std::ostringstream o;