In this paper, waveform preserving coding technique is proposed for the bio-signals based on wavelet transform local maxima representation. In order to efficiently encode the bio-signal, it utilize the inherent property of bio-signals that sharp waves corresponding to the local maxima in wavelet domain contain the most of the clinically significant information in general. The testing sets of ECG and EEG are experimented to select the appropriate wavelet basis and to demonstrate the usefulness regarding to coding efficiency. The spline basis is more suitable in designing the coder than the Harr basis since the spline basis produces less number of local maxima than the Harr basis. The proposed wavelet method based on spline basis outperforms the conventional subband coding technique in terms of wave form degradation and coding efficiency. The actual transmission experiment using external communication network and the general personal computer demonstrates the applicability to telemedicine system handling the bio-signals.