This study has developed a fault-tolerant controller that is able to recover a quadrotor from arbitrary initial orientations and angular velocities, despite the complete failure of a rotor. This cascaded control method includes a position/altitude controller, an almost-global convergence attitude controller, and a control allocation method based on quadratic programming. As a major novelty, a constraint of undesirable angular velocity is derived and fused into the control allocator, which significantly improves the recovery performance. For validation, we have conducted a set of Monte-Carlo simulation to test the reliability of the proposed method of recovering the quadrotor from arbitrary initial attitude/rate conditions. In addition, real-life flight tests have been performed. The results demonstrate that the post-failure quadrotor can recover after being casually tossed into the air.