  Let $F$ be an infinite field, and let $M_{n}(F)$ be the algebra of $n\times
n$ matrices over $F$. Suppose that this algebra is equipped with an elementary
grading whose neutral component coincides with the main diagonal. In this
paper, we find a basis for the graded polynomial identities of $M_{n}(F)$ with
the transpose involution. Our results generalize for infinite fields of
arbitrary characteristic previous results in the literature which were obtained
for the field of complex numbers and for a particular class of elementary
G-gradings.
