This paper puts forward a projection technique for accurately calculating solutions of large Quadratic Eigenvalue Problem. The aim here is to stabilize the complex eigensolutions whilst reducing residual errors, especially when considering significant damping contribution or asymmetric stiffness matrices. Hence, more confident results can be obtained in the frequency band of interest. To achieve this, high order modes, calculated using the homotopy perturbation technique, are introduced in the projection step of the classical method. This numerical proposal is a generalization of the classical projection, based only on normal modes of the associated undamped problem. To evaluate the efficiency of the suggested method, a finite element application dedicated to a friction-induced vibration problem is investigated.