Partial monitoring is an online learning model where in every time step, after a learner and an opponent choose their actions, the loss and the feedback for the learner is calculated based on a loss and a feedback function, both of which are known to the learner ahead of time. As in other online learning scenarios, the goal of the learner is to minimize his cumulative loss. In this paper we present and analyze a new algorithm for locally observable partial monitoring games. We prove that the expected regret of our algorithm is of O(√N′T), where T is the time horizon and N′ is the size of the largest point-local game. The most important improvement of this bound compared to previous results is that it does not depend directly on the number of actions, but rather on the structure of the game.