Let G be a finite permutation group on Ω. An ordered sequence of elements Ω, (ω1,…,ωt), is an irredundant base for if the pointwise stabilizer G(ω1,…,ωt) trivial and no point fixed by its predecessors. If all bases have same size we say that IBIS group. In this paper show primitive IBIS, then it must almost simple, affine-type, or diagonal type. Moreover prove diagonal-type groups only isomorph...