This paper improves on a noted square-root RTS Kalman smoothing algorithm proposed by Park and Kailath for the application purpose. This improved square-root RTS algorithm is able to additionally accommodate arbitrary exogenous known input, as such case is quite common in the real-world applications. In addition, hyperbolic Householder transformations are employed to avoid the computation of the difference of two positive semi-definite matrices. The Givens rotations based unitary transformations are further used to make the resulting algorithm have higher computational efficiency. The relevant implementation steps of this algorithm is also addressed. Finally, a numerical simulation is given to verify this improved algorithm.