This study exploits the closure property of the converse convolution operator to come up with a hybrid Clayton-Frank Archimedean copula for two random variables. Pairs of random variables were generated and the upper tail observation of the cumulative distribution function (CDF) was used to assess the right skew behavior of the proposed model. Various values of the converse convolution operator were used to see their effect on the proposed model. The simulation covered lengths n=10i,  i=2,3,4,5, and 6. The proposed model was compared with about 40 other bivariate copulas (both Archimedean and elliptical). The proposed model had parameters that spanned the entire real line, thus removing restrictions on the parameters. The parameters theta and omega were varied for a selected interval and the hybrid Clayton-Frank model was, in most cases, found to outperform the other copulas under consideration.