The random forest algorithm could be enhanced and produce better results with a well-designed and organized feature selection phase. The dependency structure between the variables is considered to be the most important criterion behind selecting the variables to be used in the algorithm during the feature selection phase. As the dependency structure is mostly nonlinear, making use of a tool that considers nonlinearity would be a more beneficial approach. Copula-Based Clustering technique (CoClust) clusters variables with copulas according to nonlinear dependency. We show that it is possible to achieve a remarkable improvement in CPU times and accuracy by adding the CoClust-based feature selection step to the random forest technique. We work with two different large datasets, namely, the MIMIC-III Sepsis Dataset and the SMS Spam Collection Dataset. The first dataset is large in terms of rows referring to individual IDs, while the latter is an example of longer column length data with many variables to be considered. In the proposed approach, first, random forest is employed without adding the CoClust step. Then, random forest is repeated in the clusters obtained with CoClust. The obtained results are compared in terms of CPU time, accuracy and ROC (receiver operating characteristic) curve. CoClust clustering results are compared with K-means and hierarchical clustering techniques. The Random Forest, Gradient Boosting and Logistic Regression results obtained with these clusters and the success of RF and CoClust working together are examined.