This study investigates the discrete extended Kalman filter as applied to multibody systems and focuses on accurate formulation of the state-transition model in the framework. The proposed state-transition model is based on the coordinate-partitioning method and linearization of the multibody equations of motion. The approach utilizes the synergies between the integration of states and estimator covariances without overly simplifying the integrator structure. The proposed method is analyzed with a forward dynamics analysis of a four-bar mechanism. The results show that the stability of the state-transition model in the forward dynamics analysis is significantly enhanced with the proposed method compared with the forward Euler-based methods. The computational efficiency of the novel method was significantly lower in comparison to forward Euler-based methods, which was found to be mainly due to the computation of the Jacobian matrix of the nonlinear state equation. However, the increase in computational cost can be considered acceptable in Kalman-filtering applications, where the exact Jacobian of the state equation is needed.