New formulation of relativistic wave equations (RWE) for massive particleswith arbitrary half-integer spins s interacting with external electromagneticfields are proposed. They are based on wave functions which are irreducibletensors of rank $n ($n=s-\frac12$) antisymmetric w.r.t. n pairs of indices,whose components are bispinors. The form of RWE is straightforward and free ofinconsistencies associated with the other approaches to equations describinginteracting higher spin particles.
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