This work focuses on the fixed-time leader-following flocking for multi-agent systems. Different from the previous continuous inherent dynamic $f(x_{i},v_{i},t)$ for agent $i$, a new nonlinear discontinuous one is firstly proposed in this paper. Employing non-smooth techniques, graph theory and fixed-time stability theory, the fixed-time leader-following flocking is achieved. Moreover, an upper bound of the settling time is independent of initial states. In addition, two illustrative examples are given to verify...