The peregrine falcon (Falco peregrinus) is known for its extremely high speeds during hunting dives or stoop. Here we demonstrate that the superior manoeuvrability of peregrine falcons during stoop is attributed to vortex-dominated flow promoted by their morphology, in the M-shape configuration adopted towards the end of dive. Both experiments and simulations on life-size models, derived from field observations, revealed the presence of vortices emanating from the frontal and dorsal region due to a strong spanwise flow promoted by the forward sweep of the radiale. These vortices enhance mixing for flow reattachment towards the tail. The stronger wing and tail vortices provide extra aerodynamic forces through vortex-induced lift for pitch and roll control. A vortex pair with a sense of rotation opposite to that from conventional planar wings interacts with the main wings vortex to reduce induced drag, which would otherwise decelerate the bird significantly during pull-out. These findings could help in improving aircraft performance and wing suits for human flights.