Abstract: As a new technique of image or signal compression, wavelet transform have recently been introduced in subband coding. The technique has the flexibility of a few freedoms in wavelet basis selection. This is one of its advantages over classical technique as the discrete consine transform. It also poses a problem of the optimal wavelet which is adapted to given signal. The problem of the optimal orthonormal wavelet is investigaed in the paper. The optimal objective measure is the coding gain Gsbc. For a stationary random signal the optimal wavelet only depend on the power spectral density (PSD) of the signal. The calculated results corresponding to three typical PSD are given.