This paper concerns with a new linear finite impulse response (FIR) filter called the receding horizon unbiased FIR (RHUF) filter for the state estimation in discrete-time state space models. To obtain the RHUF filter, linearity, unbiasedness and FIR structure will be required beforehand in addition to a performance criteria of minimum variance. The RHUF filter is obtained by directly solving an optimization problem with the unbiasedness constraint. The RHUF filter has time-invariance and deadbeat properties. The RHUF filter is represented in both a batch form and an iterative form. it is shown that the RHUF filter is equivalent to the existing receding horizon Kalman FIR (RHKF) filter whose optimality is not clear to understand. The former is more systematic and logical, while the latter is heuristic due to handling of infinite covariance of the initial state information.