  In this paper, we establish congruences (mod $p^2$) involving the
quadrinomial coefficients $\dbinom{np-1}{p-1}_{3}$ and
$\dbinom{np-1}{\frac{p-1}{2}}_{3}$. This is an analogue of congruences
involving the trinomial coefficients $\dbinom{np-1}{p-1}_{2}$ and
$\dbinom{np-1}{\frac{p-1}{2}}_{2}$ due to Elkhiri and Mihoubi.
