The position-space renormalization group method is employed to investigate the order-disorder transitions in the W(112)p(2×1)-O system. The recursion relations are based on the periodically continued cluster of four cells with four sites each. We consider the pairwise interactions between nearest, nextnearest neighbours as well as the three-particle and four-particle interactions and formulate the relationships between renormalized coupling parameters K′a and interaction constants Ka. From the renormalization iteration, we find the fixed point Ka* and the critical temperature Tc for various monolayer coverages. The phase diagram of the W(112)p(2×l)-O overlayer obtained is found to be in agreement with the existing experimental results.