The specific features of backward stimulated Raman scattering (BSRS) of a short modulated (multi-frequency) laser pulse in underdense plasmas are studied. The effect of resonant suppression of the BSRS of higher frequency pulse components is explored. For an arbitrary pair of pulse components, in the conditions of weak coupling, it is demonstrated that the backscattering of a higher frequency laser pulse component is a five-wave resonant process at a frequency difference between the components close to the double plasma frequency. In the conditions of strong coupling the backscattering of neither pulse component is suppressed and the spectrum of the instability is not connected immediately with the details of a spectrum of a laser pulse. Numerical modelling of the BSRS of a multi-frequency laser pulse is in complete agreement with the analytical predictions.