Résumé
We continue the study of the algebras satisfying an identity of the shape aX(2)X(2)+bX(4)-X-3-X-2-X, we introduce here the case a+b=1, ab0, =2, and + = -1. By studying a 26x27 linear system, we show that this class admits a partition into six parts among which four correspond to algebras not verifying other identity of degree 4. In this article we study these four algebras. We show they satisfy principal and plenary train identities of rank>4, we determine the algebras admitting an idempotent and we give their Peirce decompositions in the two cases: with and without idempotent.