Abstract: By using the recursive formula of GOP, the separative matrices of GOP, which have a nice structure and an elegant recursive formula, are introduced at first time. Applying the property of the separative matrices, the paper presents a new approach to the solution of convolution integral. Two examples are included to demonstrate the validity and applicability of the approach. Moreover the separative matrices can be used for the identification of impulse response and the optimal design of linear servomechanisms as well as the analysis, parameter estimation and optimal control of systems with time-delay.