This paper proposes a novel grouping decision approach for blind deconvolution of FIR channels with binary sources. First, necessary and sufficient conditions for recoverability are derived. For single-input systems, a new deterministic algorithm based on grouping and decision is propose to recover the source up to a delay. Then the algorithm is extended to deal with high noise case and long decaying channel case. Furthermore blind deconvolution for multi-input systems also can be carried out as with the case of single input systems. All sources can be recovered sequentially. Finally, the validity and performance of the algorithms are illustrated by several simulation examples.