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In this paper, generalized functional projective synchronization of a new hyperchaotic system with uncertain parameters is investigated by using adaptive control technique. Based on the Lyapunov stability theory, the adaptive controllers are designed to make the states of two identical new hyperchaotic systems asymptotically synchronize up to the desired scaling function matrix. The parameter update law for estimating the unknown parameters of the systems is also derived. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed synchronization scheme.