A nonorthogonal theory is used to study the non-Hermitian character of the excess noise in gain-guided transient Raman amplifiers. We calculated the output of the gain-guided transient Raman scattering based on a nonorthogonal mode expansion. We found that the excess noise in a transient gain-guided amplifier increases nonlinearly from 0 (and the Petermann factor nonlinearly from 1) and that the evolution depends mainly on the integrated energy of the pump laser pulse.