The paper presents a formulation of small-strain rate-independent single-crystal plasticity in the multisurface format and points out aspects of its numerical implementation. The key problem of the rate-independent formulation of single crystal plasticity is the possible occurrence of redundant constraints due to linear-dependent active slip systems. This results in a possible non-uniqueness of the set of active slip systems. In order to overcome this problem, we propose here in line with recent research developments a solution procedure for the determination of the incremental active slips based on a particularly chosen generalized inverse of the Jacobian of the active yield criterion functions. The performance and physical acceptance of the proposed formulation is demonstrated for two representative numerical model problems.