Abstract:Based on the real representation of quaternionꎬ combined with the structural characteristics of the claw matrixꎬ and through the Kronecker product of matricesꎬ the constrained quaternion matrix equation AXB=C of the claw matrix is transformed into the unconstrained real matrix equation.Then the necessary and sufficient conditions for the existence of a paw form matrix solution and a self ̄conjugate paw form matrix solution of the equation are obtained. Finallyꎬthe optimal approximation of the minimum Frobenius norm for the given quaternion claw matrix in the given solution set is obtained.