We consider remote state estimation over a packet-dropping network. A new suboptimal filter is derived by minimizing the mean squared estimation error. The estimator is designed by solving one deterministic Riccati equation. Convergence of the estimation error covariance and mean square stability of the estimator are proved under standard assumptions. It is shown that the new estimator has smaller error covariance and has wider applications when compared with the linear minimum mean squared error estimator. One of the key techniques adopted in this technical note is the introduction of the innovation sequence for the multiplicative noise systems.