Using projection theory and a decomposition in canonical form, a new recursive reduced-order filter for descriptor discrete-time stochastic linear systems with correlated noises is given by transferring system with correlated noised to that with independent noises. It can reduce the computational burden, and is suitable for real-time applications. posed Compared with redured-order filter for descriptor systems with independent noises in exsting literature, the proreduced-order filter has on additional gain at current time. Simulation example proves the effectiveness,