In this letter, unlike the previous work in [2], the optimal power allocation in a non-orthogonal, amplify-and-forward (AF) relay-assisted transmission is investigated in the uplink. Here, the inter-user-interference among the signals from MTs and relays exists due to non-zero interference suppression factor (ISF), i.e., finite spreading factor. In this letter, we show that the optimal solution to achieve a ‘max-min fairness’ among mobile terminals can be alternatively obtained by solving its inverse problem. The impact of various ISFs as well as the Jain's fairness is investigated in comparison with the equal power allocation.