Subresultants are defined usually by means of subdeterminants of the Sylvester matrix. This paper gives an explicit and simple representation of the subresultants in terms of subdeterminants of the Bézout matrix and thus provides an alternative definition for subresultants. The representation and the lower dimensionality of the Bézout matrix lead to an effective technique for computing subresultant chains using determinant evaluation. Our preliminary experiments show that this technique is computationally superior to the standard technique based on pseudo-division for certain classes of polynomials.