Raman backward scattering is investigated in the interaction of linearly polarized ultra short laser pulse with a homogenous cold underdense magnetized plasma by taking into account the relativistic effect and the effect of nonlinearity up to third order. The plasma is embedded in a uniform magnetic field perpendicular to both of propagation direction and electric vector of the radiation field. Nonlinear wave equation is set up and differential equations, which model the instability, are derived. Using of the Fourier transformation, analytical solutions are obtained for a set of physically relevant initial conditions and the temporal growth rate of instability is calculated. Results are significantly different in comparison with lower order computations. The growth rate of backward Raman scattering shows an increase due to the presence of external magnetic field as well as nonlinear effects.
