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This paper introduces a very fast search algorithm of algebraic fixed codebook in CELP-based speech codecs. The proposed method searches codebook pulses sequentially, and recomputes the fixed codebook gain, the so-called backward filtered target vector, and a certain reference signal after each new pulse is determined. This results in a significant complexity reduction compared to existing methods while preserving the same speech quality. The presented algorithm is used in the new embedded speech and audio codec (G.EV-VBR) being currently standardized by the ITU-T.