A new explicit method for the discretization of nonlinear continuous-time systems is presented. A nonlinear discrete-time model is obtained by integrating a Carleman approximation of the original continuous-time system. In contrast to conventional explicit discretization methods, the proposed Carleman discretization does not deteriorate rapidly as the sampling period increases. Examples of open-loop and deadbeat closed-loop responses of an isothermal continuous stirred tank reactor reveal the advantages of the proposed discretization scheme.