Abstract
In this note we extend an irreducibility criterion of polynomial over finite fields. We prove the irreducibility of the polynomial P(Y) = Y-n + lambda Y-n-1(n-1) + lambda Y-n-2(n-2) + ... + lambda Y-1 + lambda(0), such that lambda(0) not equal 0, deg lambda(n-2) = 2deg lambda(n-1) + l > deg lambda(i), for all i not equal n - 2 and odd integer l.