[en] Theory of average recoil polarization in the muon capture by nuclei with arbitrary spin is discussed. The analysis is performed to determine a contribution of weak interactions into the polarization value taking into account the hyperfine structure of mesoatom. The average recoil polarization is calculated from canonical representation of density transition matrix which is constructed by means of density matrix for the initial state of system and amplitude of nuclear transition given in multipole expansion. The cases of direct transition to the ground state of a daughter nucleus and a cascade transition are considered. Here an excited state occurs at the muon capture which goes to the ground state by an electromagnetic decay. Taking the ⁹Be nucleus as an example simultaneous direct and cascade transitions are analyzed. It turns out that for the muon capture in the ⁹Be nucleus the participation of cascade transition leads to extinguishing value of the average nuclear recoil polarization. This effect influences determining weak interaction form factors