The canonic signed digit code used to represent the coefficients of power-of-two FIR (2PFIR) filter is nonuniformly distributed in the coefficient space. This paper proposed a neighboring full-search algorithm to design the multiplierless FIR filter such that this nonuniform distribution characteristics is exploited. The proposed procedure can provide a multiplierless FIR filter with fewer numbers of nonzero digits compared with others due to the joint consideration in finding and quantizing the FIR filter coefficients and the exhaustive search nature of the proposed algorithm.