This paper discusses a novel method of exact discretization obtaining an equivalent difference equation whose solution is equal to the solution of a differential equation at discrete periodic points. The method differs from the existing method in needing no solutions of the differential equations. The z-transform of the equivalent difference equation is produced from applying the s-z transform of substituting (s - /spl alpha/) by (1 - e/sup /spl alpha/T/ z/sup -1/) to the Laplace transform of a differential equation. Then, the equivalent difference equation of the new representation is obtained from the z-transform. The method is applied to general linear constant-coefficient differential equations and to some examples including the nonlinear differential equation of the logistic equation which represents chaotic behavior.