This paper performs further improvement to a distributed algorithm for solving linear algebraic equations via multi-agent networks recently developed by Mou et al., in which all agents' states converge exponentially fast to the same solution to a group of linear equations by assuming each agent knows only part of the linear equations and its nearby neighbors' states. We first prove that the algorithm proposed by Mou et al. with special initialization is able to achieve the solution that is closest to a given point in the Euclidean distance. Second, we eliminate the required initialization step used by Mou et al. by a modification to the update equation. Both analytical and numerical results are provided for validation.