This paper presents a new multistage comb-rotated sinc (RS) decimator with a sharpened magnitude response. Novelty of this paper is that the multistage structure has more design parameters that provides additional flexibility to the design procedure. It uses different sharpening polynomials and different cascaded comb filters at different stages. As the comb filters at the latter stages are of lower order than that of the original comb filter, the use of more complex sharpening polynomials at latter stages is possible. This leads to an improvement of the frequency characteristic without a significant increase in the complexity of the overall filter. The comb filter of the first stage is realized in a non-recursive form and can be implemented in a computationally efficient form by making use of the polyphase decomposition of the transfer function in which the subfilters operate at a lower rate that depends on the down-sampling factor employed in the first stage. In addition, both multipliers of the rotated sinc (RS) filter of the second stage work at a lower rate.