The wave equations in anisotropic media are not solved easily. The major difficulty is due to the fact that electric and magnetic fields are coupled, and permittivity and permeability are represented by matrices. In the special case that the anisotropy comes from only one of permittivity or permeability, the solution can be obtained analytically, with the so-called dyadic Green`s function, but in general case the solutions of the equations are possible only through the numerical calculation. The typical wave equations in anisotropic media cannot be decoupled because of matrix structure of the anisotropy. However the slight different derivation of wave equation from Maxwell`s equations gives the new decoupled version of the wave equations. The Fourier transformed tensor Green`s function is obtained for this new equation, When there is a source term.