EPR spectra have been recorded in very high fields up to 25 T, and at high frequency up to 525 GHz, on a polycrystalline sample of $[{\mathrm{Mn}}_{12}{\mathrm{O}}_{12}{(\mathrm{C}\mathrm{H}}_{3}{\mathrm{C}\mathrm{O}\mathrm{O})}_{16}{(\mathrm{H}}_{2}{\mathrm{O})}_{4}{]\mathrm{\ensuremath{\cdot}}2\mathrm{C}\mathrm{H}}_{3}{\mathrm{COOH}\mathrm{\ensuremath{\cdot}}4\mathrm{H}}_{2}\mathrm{O}$ (Mn12ac), a molecular cluster behaving like a nanomagnet. The simulation of the spectra has provided an accurate determination of the parameters of the spin Hamiltonian $H={\ensuremath{\mu}}_{B}\mathbf{H}\ensuremath{\cdot}\mathbf{g}\ensuremath{\cdot}\mathbf{S}+D[{S}_{z}^{2}\ensuremath{-}1/3S(S+1)]{+B}_{4}^{0}{O}_{4}^{0}{+B}_{4}^{4}{O}_{4}^{4},$ where ${O}_{4}^{0}{=35S}_{z}^{4}\ensuremath{-}{30S(S+1)S}_{z}^{2}{+25S}_{z}^{2}\ensuremath{-}{6S(S+1)+3S}^{2}{(S+1)}^{2}$ and ${O}_{4}^{4}{=1/2(S}_{+}^{4}{+S}_{\ensuremath{-}}^{4}):D=\ensuremath{-}0.46(2)$${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ ${B}_{4}^{0}=\ensuremath{-}2.2(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ and ${B}_{4}^{4}=\ifmmode\pm\else\textpm\fi{}4(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$${\mathrm{ }\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}.$ The presence of the fourth-order term in the total spin justifies the irregularities in the spacing of the jumps, recently observed in the hysteresis loop of Mn12ac and attributed to acceleration of the relaxation of the magnetization due to quantum tunneling between degenerate $M$ states of the ground $S=10$ multiplet of the cluster. The term in ${(S}_{+}^{4}{+S}_{\ensuremath{-}}^{4})$ is responsible for the transverse magnetic anisotropy and plays a crucial role in the mechanism of quantum tunneling. The high-frequency-EPR spectra have shown its presence and quantified it.