Sampling-based dimensionality reduction technique•Eliminating linearly redundant combined dimensions•Providing a convenient way to generate correlated multivariate random variables•Maintaining the integrity of the original information•Reducing the dimension of data space without losing important information The recent trends in collecting huge and diverse datasets have created a great challenge in data analysis. One of the characteristics of these gigantic datasets is that they often have significant amounts of redundancies. The use of very large multi-dimensional data will result in more noise, redundant data, and the possibility of unconnected data entities. To efficiently manipulate data represented in a high-dimensional space and to address the impact of redundant dimensions on the final results, we propose a new technique for the dimensionality reduction using Copulas and the LU-decomposition (Forward Substitution) method. The proposed method is compared favorably with existing approaches on real-world datasets: Diabetes, Waveform, two versions of Human Activity Recognition based on Smartphone, and Thyroid Datasets taken from machine learning repository in terms of dimensionality reduction and efficiency of the method, which are performed on statistical and classification measures.