{We present a new method of matching the Constrained Monte Carlo (CMC) algorithm to next-to-leading order matrix elements. In such matching, one must simultaneously treat the infra-red singularities of the matrix element and double counting issues between the two contributions. In the proposed method these two issues are dealt with by a specially defined counterterm. This counterterm is analyzed in detail and the connection of the CMC algorithm and formal factorization theorems is given. This counterterm also allows many new processes to be quickly integrated into the algorithm as the application of the counterterm can be done at the matrix element generation level and all residual issues in the parton shower are universal.}

PACS numbers: 12.38.--t, 12.38.Bx, 12.38.Cy