In this correspondence, a method for designing perfect reconstruction (PR) prototypes for paraunitary cosine-modulated filter banks is presented. The design procedure is based on a subspace approach that allows linear combinations of even-length linear-phase PR prototype filters in such a way that the resulting filter is also a linear-phase PR prototype. Within a given subspace, the weights of the optimal linear combination can easily be computed via an eigenanalysis. The filter design is carried out iteratively while the PR property is guaranteed throughout the design process. No nonlinear optimization routine is needed. As a special case, the proposed approach allows the design of discretecoefficient prototypes, which are of great interest for efficient hardware implementations. Index Terms- Cosine modulation, discrete coefficients, filter banks, integer coefficients.