In this work, a novel model free adaptive control method based on a mathematical algorithm named double successive projection (DSP-MFAC) is proposed, from which it can be inferred that conventional MFAC algorithm is only a special case of DSP-MFAC with the Cartesian product of the output and the input Hilbert space. For a general unknown nonlinear system, an innovative partial form dynamic linearization (PFDL) technique is first presented based on a new concept named pseudo gradient (PG). Then, the controller for the system is designed based on the PG with the aid of a novel DSP algorithm modified from the conventional successive projection algorithm. Consequently, the structures of the controller and its parameters estimator are symmetric similar, which makes the control performance become stable. Meanwhile, the convergence of DSP-MFAC for a regulation problem of a class of nonlinear discrete systems are guaranteed by rigorous mathematical analysis under several reasonable assumptions. Furthermore, numerical simulation results show that DSP-MFAC is effective and applicable.