Abstract: The symmetrical wavelets with linear phase are extensively applied in signal or image compression. It has the flexibility in basis selection. This makes it possible to design signaladapted wavelet. The problem of optimal symmetrical wavelet in subband coding is investigated in the paper. The optimal objective measure is the coding gain Gsbc. For a stationary random signal the optimal wavelet depends only on the power spectral density (PSD) of the signal. The calculated results corresponding to three typical PSD are given.