A new linear prediction analysis method for multichannel signals was devised, with the goal of enhancing the compression performance of the MPEG-4 Audio Lossless Coding (ALS) compliant encoder and decoder. The multichannel coding tool for this standard carries out an adaptively weighted subtraction of the residual signals of the coding channel from those of the reference channel, both of which are produced by independent linear prediction. Our linear prediction method tries to directly minimize the amplitude of the predicted residual signal after subtraction of the signals of the coding channel, and the method has been implemented in the MPEG-4 ALS codec software. The results of a comprehensive evaluation show that this method reduces the size of a compressed file. The maximum improvement of the compression ratio is 14.6% which is achieved at the cost of a small increase in computational complexity at the encoder and without increase in decoding time. This is a practical method because the compressed bitstream remains compliant with the MPEG-4 ALS standard.