Quantum steering in a global state allows an observer to remotely steer a subsystem into different ensembles by performing different local measurements on the other part. We show that, in general, this property cannot be perfectly cloned by any joint operation between a steered subsystem and a third system. The perfect cloning is viable if and only if the initial state is of zero-discord. We also investigate the process of cloning the steered qubit of a Bell state by using a universal cloning machine. Einstein-Podolsky-Rosen (EPR) steering, which is a type of quantum correlation existing in the states without a local-hidden-state model, can be found in both of the copy subsystems. This breaks the recent conclusion of no-cloning of quantum steering (EPR steering) in [npj Quantum Inf. 2, 16020 (2016)] based on a mutual information criterion for EPR steering.

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