  Let $G$ be a finite permutation group on $\Omega$. An ordered sequence of
elements of $\Omega$, $(\omega_1,\dots, \omega_t)$, is an irredundant base for
$G$ if the pointwise stabilizer $G_{(\omega_1,\dots, \omega_t)}$ is trivial and
no point is fixed by the stabilizer of its predecessors. If all irredundant
bases of $G$ have the same size we say that $G$ is an IBIS group. In this paper
we show that if a primitive permutation group is IBIS, then it must be almost
simple, of affine-type, or of diagonal type. Moreover we prove that a
diagonal-type primitive permutation groups is IBIS if and only if it is
isomorphic to $PSL(2,2^f)\times PSL(2,2^f)$ for some $f\geq 2,$ in its diagonal
action of degree $2^f(2^{2f}-1).$
