Abstract: The separative matrices of shifted Chebyshev polynomials of the first and second kinds, which have a nice structure and an elegant recursive formula, are introduced at the first time. By using the property of the separative matrices, a new approach to the convolution integral is presented. Two examples are included to demonstrate the validity and applicability of the approach. In addition, the separative matrices can be applied to the identification of impulse response of linear systems and the optimal design of linear servomachanisms.