This paper proposed a solution to the Finite Escape Time problem in H∞ Filter based Simultaneous Localization and Mapping problem. Finite escape time has been one of the obstacle that holding the realization of H∞ Filter in many applications. For this reason, a method of decorrelating some of the updated state covariance of the filter is suggested to avoid the finite escape time from occurred during mobile robot estimations. Two main cases are investigated in this paper to observe the filter performances which are the unstable partially observable and stable partially observable H∞ Filter-SLAM. The simulation results have shown convincing outcomes to the overall estimation, which can prevent the finite escape time in the estimation especially for the stable partially observable H∞ Filter-SLAM case.