A new speech enhancement algorithm for speech corrupted by slowly varying additive colored noise is suggested based on a state-space signal model. Due to the FIR structure and the unimportance of long-term past information, the receding horizon (RH) FIR filter known to be a best linear unbiased estimation (BLUE) filter is utilized in order to obtain noise-suppressed speech signal. As a special case of the colored noise problem, the suggested approach is generalized to perform the single blind signal separation of two speech signals. It is shown that the exact speech signal is obtained when an incoming speech signal is noise-free.