A new approach to the coding of speech signals is presented. Called the Block Adaptive Coder, it reduces the coder complexity and computational burden and increases the transmission rate of the data. In the classical Adaptive Predictive Coding methods, the predictor coefficients along with the residual signal, are to be transmitted to the receiver. In the present work, this residual signal is not transmitted, which in turn reduces the coder complexity at the transmitter. But, the first few sample values have to be transmitted every block. The predictor is updated, if necessary, based on the correlation between the input samples. The technique is verified by simulation and the results prove the simplicity of the coder as well as the reduction in computation.