  The recoil, vacuum polarization and electron vertex corrections of first and
second orders in the fine structure constant $\alpha$ and the ratio of electron
to muon and electron to \alpha-particle masses are calculated in the hyperfine
splitting of the $1s^{(e)}_{1/2}2s^{(\mu)}_{1/2}$ state of muonic helium atom
(\mu e ^4_2He) on the basis of a perturbation theory. We obtain total result
for the muonically excited state hyperfine splitting $\Delta \nu^{hfs}=4295.66$
MHz which improves previous calculations due to the account of new corrections
and more accurate treatment of the electron vertex contribution.
