In a previous paper [J. Non-Classical Logic 7, No. 1/2, 145-154 (1990; Zbl 0726.03018)], the authors proved that the paraconsistent logic \(P_ 1\), introduced by \textit{A. M. Sette} [Math. Jap. 18, 173-180 (1973; Zbl 0289.02013)], is algebraizable. In this paper, a characterization of these algebras along with a complete description of the free algebras in \(n\) generators is done. The interesting peculiarity is that the latter is not a congruence-modular quasi-variety.