For a binary matrix X, the Boolean rank br(X) is the smallest integer k for which X equals the Boolean sum of k rank-1 binary matrices, and the isolation number i(X) is the maximum number of 1s no two of which are in a same row, column and a 2x2 submatrix of all 1s. We continue Lubiw's study of firm matrices, X is firm if i(X)=br(X) and this equality holds for all its submatrices. We show that a stronger concept of superfirmness of X is equivalent to having no odd holes in a graph defined from X. Then we introduce two matrix operations that lead to generalised binary matrices and use them to derive four infinite classes of minimally non-firm matrices, matrices which are not firm but all of their proper submatrices are.