Considering the general problem of updating switches in a software defined network architecture, temporary loops can occur in the case of inappropriate scheduling of node updating order. This problem and others like a black hole also called consistency problems must be avoided. This work focuses mainly on round-based approaches, especially in relaxed loop freedom. The round-based solution has gained more attraction in literature due to the absence of impact on switch’s resource than the stamping/tagging solution. However previous works focus on rapidly computing the update schedule or minimizing the schedule, and did not provide tradeoff between rapidly computing the schedule and reducing the make span of the schedule. In this work we have developed a new enhancement of the Peacock algorithm combining a fast update schedule computing and reducing the schedule make span to at most \({2log}_{2}\left(n\right)-1\) rounds.