In the present paper, we validate and assess a correlation functional based on the so-called meta generalized gradient approximation, whose form and parameters are entirely derived only from first-principles criteria. In particular, we have carried out a detailed comparison with the most common, parametrized correlation functionals. Next, we propose a new model in which the correlation functional proposed by Kriger, Chen, Iafrate, and Savin is integrated in a hybrid Hartree-Fock/density functional theory scheme. In such approach only one, or two in the G2-optimized version, parameters are adjusted on experimental data, all the others being derived from purely theoretical considerations. The results obtained for a set of molecular properties, including H-bonded complexes, proton transfer model, S(N)2 reaction and magnetic properties, are satisfactory and comparable, if not better, with those delivered by the most common functionals including heavy parametrization. The way in which the whole functional is derived and the few empirical parameters used make the new exchange-correlation functional widely applicable.