The downstream region of a collisionless quasiparallel shock is structured containing bulk flows with high kinetic energy density from a previously unidentified source. We present Cluster multispacecraft measurements of this type of supermagnetosonic jet as well as of a weak secondary shock front within the sheath, that allow us to propose the following generation mechanism for the jets: The local curvature variations inherent to quasiparallel shocks can create fast, deflected jets accompanied by density variations in the downstream region. If the speed of the jet is super(magneto)sonic in the reference frame of the obstacle, a second shock front forms in the sheath closer to the obstacle. Our results can be applied to collisionless quasiparallel shocks in many plasma environments.