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The square-root unscented Kalman filter (SRUKF) for state estimation probably encounters the problem that Cholesky factor update of the covariance matrices cant be implemented when the zeroth weight of sigma points is negative or the numerical computation error becomes large during the filtering procedure. Consequently the filter becomes invalid. An improved SR-UKF algorithm (ISRUKF) is presented for state estimation of arbitrary nonlinear systems with linear measurements. It adopts a modified form of predicted covariance matrices, and modifies the Cholesky factor calculation of the updated covariance matrix originating from the square-root covariance filtering method. Discussions have been given on how to avoid the filter invalidation and further error accumulation. The comparison between the ISR-UKF and the SR-UKF by simulation also shows both have the same accuracy for state estimation. Finally the performance of the improved filter is evaluated under the impact of model mismatch. The error behavior shows that the ISR-UKF can overcome the impact of model mismatch to a certain extent and has excellent trace capability.