  We calculate corrections of order $\alpha^3(Z\alpha)E_F$ to hyperfine
splitting in muonium generated by the gauge invariant set of diagrams with
polarization insertions in the light by light scattering diagrams. This
nonrecoil contribution turns out to be -2.63 Hz. The total contribution of all
known corrections of order $\alpha^3(Z\alpha)E_F$ is equal to -4.28 Hz.
