In this paper we present a new method which allows complete decomposition of the optimal global Kalman filter for linear singularly perturbed systems into pure-slow and pure-fast local optimal filters both driven by the system measurements. The method is based on the exact decomposition of the global singularly perturbed algebraic Riccati equation into pure-slow and pure-fast local algebraic Riccati equations. An F-8 aircraft example demonstrates the proposed method.