This paper presents the optimal two-stage Kalman filter for systems that involve noise-free observations and constant but unknown bias. Like the full-order separate-bias Kalman filter presented in 1969 [1], this new filter provides an alternative to state vector augmentation and offers the same potential for improved numerical accuracy and reduced computational burden. When dealing with systems involving accurate, essentially noise free measurements, this new filter offers an additional advantage, a reduction in filter order. The optimal separate-bias reduced order estimator involves a reduced-order filter for estimating the state, the order equalling the number of states less the number of observations.