Li and Zhou propose simpler Petri net controllers based on the concept of elementary siphons (generally much smaller than the set of all strict minimum siphons (SMSs) in large Petri nets) to minimise the addition of control places. SMSs can be divided into two groups: elementary and dependant; characteristic T-vectors of the latter are linear combinations of that of the former. A T-vector eta is associated with each siphon S such that eta(i) is the number of tokens gained in or lost from S by firing transition t(i) once. A dependent siphon S-0 strongly depends on elementary siphons S-1, S-2, horizontal ellipsis , S-k if eta(0) = a(1)eta(1) + a(2)eta(2) + ... + a(k)eta(k) with all a(i) (i = 1, 2, 3, horizontal ellipsis , k) positive. S-0 is a weakly dependent siphon if some a(i) is negative. The T-vectors (resp. number) for elementary siphons are mutually independent (linear to the size of the net). In an earlier paper, we show that there exists a third siphon S-3 such that eta(beta) = eta(1) + eta(2) - eta(3). This equation (called eta relationship) plays an important role for optimal control of weakly dependent siphons. However, it assumes that all above S span between exactly two processes. For a well-known benchmark, however, most dependent siphons span more than two processes. This paper improves by removing this restriction and shows that eta(beta) = eta(1) + eta(2) - eta(3) holds as long as S-1 boolean AND S-2 is another emptiable siphon.