The usual technique of the laser induced plasma spectroscopy (LIPS) spectra analysis relies on the use of calibration curves for quantitative measurements of plasma composition. However, LIPS calibration curves strongly depend on the material composition (the so-called matrix effect); thus, this standard approach to the LIPS spectra analysis is inadequate when precise information on unknown samples composition is required. In this paper we present a new procedure, based on LIPS, for calibration-free quantitative elemental analysis of materials. The new procedure, based on an algorithm developed and patented by IFAM-CNR, allows the overcoming of the matrix effect, yielding precise and accurate quantitative results without the need of calibration curves.