The pump depletion is a severe problem which hinders the laser-plasma beat-wave accelerator concept from being practical. Starting with the weak relativistic equation of beat-wave excitation of electron plasma waves, we have derived the condition for eliminating the pump depletion in the frame moving with the light pulse for arbitrary pulse shapes. It is shown that the depletion can be eliminated by a phase jump of π at the center of the pump pulse and by the appropriate choice of initial plasma density detuning. The numerical calculation have yielded the dependence of the initial detuning on the pump intensity for square pump pulses, and have supported the methods used in this paper.