A finite-time consensus protocol is proposed for multi-dimensional multi-agent systems, using direction-preserving signum controls. Filippov solutions and nonsmooth analysis techniques are adopted to handle discontinuities. Sufficient and necessary conditions are provided to guarantee infinite-time convergence and boundedness of the solutions. It turns out that the number of agents which have continuous control law plays an essential role in finite-time convergence. In addition, it is shown that the unit balls introduced by ℓp norms, where p∈ [1 , ∞] , are invariant for the closed loop.