Considering the increase in power system size and the number of PMUs, the utilization of a computationally efficient yet accurate static state estimator is crucial. The fast-decoupled WLS estimator (FD-WLS) is the most common method employed in industrial applications, thanks to its computational efficiency and ease of implementation. However, it is known that FD-WLS fails in the presence of an ill-conditioned power system, e.g., a power system with high R/X ratio and large difference between measurement error variances. This paper proposes a partitioning strategy for ill-conditioned power systems. The proposed method forms two types of subsystems, such that one can apply FD-WLS in the type-1 sub-systems, and conventional formulation of WLS should be applied in the type-2 sub-systems. The utilization of the proposed method enables a computational performance comparable to that of FD-WLS and an accuracy comparable to that of the centralized solution.