This work presents a variation of the elastic net penalization method. We propose applying a combined \(l\)₁ and \(l\)₂ norm penalization on a linear combination of regression parameters. This approach is an alternative to the \(l\)₁-penalization for variable selection, but takes care of the correlation between the linear combination of parameters. We devise a path algorithm fitting method similar to the one proposed for the least angle regression. Furthermore, a one-shot estimation technique of \(l\)₂ regularization parameter is proposed as an alternative to cross-validation. A simulation study is conducted to check the validity of the new technique.