If \(A\) is a regular interval matrix, the inverse of \(A\) is defined as that interval matrix of smallest width which contains all point inverses of \(A\). Let the inverse of \(A\) be denoted by \(B = (B_{ij})\) with intervals \(B_{ij} = [\underline{B}_{ij},\overline{B}_{ij}]\). A finite set of point matrices \(A_{yz} \in A\) is introduced where \(y\) and \(z\) are vector parameters with elements \(\pm 1\) only. It is shown that each \(\underline{B}_{ij}\) can be determined as the \((i,j)\)th element of some \(A^{-1}_{yz}\). The same holds for \(\overline{B}_{ij}\). If \(A\) is inverse stable, the parameters \(y\) and \(z\) can be characterized precisely. Furthermore, explicit formulas for \(B\) are established if the rank of the diameter matrix is one.