A receding horizon Kalman FIR filter is presented that combines the Kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown. The suggested filter is an FIR filter form which has many good inherent properties. It can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state. The suggested filter can be represented in either an iterative form or a standard FIR form. It is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat propel ty irrespective of any horizon initial condition. The validity of the suggested filter is illustrated by numerical examples.