Relativistic wave equations for interacting, massive particles with arbitrary half-integer spins

New relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins s interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank $2n$ $(n=s-\frac{1}{2})$ antisymmetric with respect to n pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles.