The existence of extended emission (EE) is an intriguing property of short-duration gamma-ray bursts, because the nature of the EE is still unclear. It might be a rising X-ray afterglow, or it could be a manifestation of the prolonged activity of a central engine. We consider short-duration gamma-ray bursts, emphasizing the common properties of both short bursts and short bursts with EE. Assuming that the EE with broad dynamic range is a common property of short bursts, we propose a two jet model which can describe both short main episode of hard spectra emission, specific for short bursts, and softer spectra EE by different off axis position of observer. The model involves a short-duration jet, which is powered by heating due to annihilation, and a long-lived Blandford–Znajek jet with a significantly narrow opening angle. Our proposed model is a plausible mechanism for short-duration burst energization. It can explain short bursts both with and without EE within a single class of progenitor.