Multi-pulse excitation model used for speech coding provides excellent quality at medium bit-rates. However it is not very suitable for producing high frequency components in speech signals. For instance, a SNR of 15 dB in the lower band (0-2 kHz) of speech can be reduced to 3 dB for the upper band (2-4 kHz) of the signal. This paper describes a new method which enhances the speech quality by improving reproduction of high frequency portions of the signal. The idea consists of splitting the total frequency range into two sub-bands by means of Quadratic Mirror Filters, and optimizing the coding in each band. Evaluations have shown that the SNR can be improved up to 9 dB in high frequency band, and an enhancement of the total speech quality is obtained.