The decentralized navigation function methodology, established in previous work for navigation of a multi-agent system with single integrator dynamics is extended to the case of double integrator. The main motivation of this work lies in the fact that acceleration control is more implementable in multiple vehicle systems than velocity control. Each agent plans its actions without knowing the destinations of the others. The stability of the overall system is guaranteed by LaSalle's Invariance Principle. The collision avoidance and global convergence properties are verified through simulations.