The inelastic cross section of relativistic charged particles with atom consists of two parts, longitudinal and transverse excitations. The transverse excitation is effective only for relativistic and small angle scattering. Fano``s dipole approximation for the transverse excitation is generalized to include optically forbidden as well as allowed excitations. And the results are compared with numerical computations for $2S_{1/2} $\to$ 2P_{1/2}$, $2P_{3/2}$, $3S_{1/2}$, $3P_{1/2}$, $3P_{3/2}$, $3D_{3/2}$, and $3D_{5/2}$ excitations of Li-like carbon and tungsten atomic ions.