The discrete-time linear filtering problem is considered where the system is constant and the noise is stationary. An optimal time-invariant linear filter is obtained in z-transfer function matrix form. The filter gives an unbiased minimum variance state estimate at the end of a given fixed filtering interval [ 0, T] This state estimate is the same as that which would be obtained using a time-varying Kalman filter, The estimate is therefore better than that which would be obtained from a Wiener filter at this time. The state estimates within the finite filtering interval can also be an improvement over those from a Wiener filter. The major advantage of this filter is that it may be easily implemented because it is time-invariant.