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This paper proposes an adaptive second order sliding mode (SOSM) control strategy to tackle nonlinear uncertain systems. For effective handling of the uncertain system, prior knowledge about the upper bound of the system uncertainty is a prerequisite for the sliding mode control (SMC). In order to remove this constraint, an adaptive tuning law based SMC was designed recently where the upper bounds of the uncertainties were not required to be known in advance. However, such controllers were found to suffer from the drawback of the high frequency chattering in the control input. In this paper an improved adaptive second order sliding mode controller is proposed to alleviate the undesired chattering phenomenon. The proposed control strategy uses an adaptive tuning law for the sliding mode controller which is of the second order. A simulation example illustrates the benefits of the proposed scheme.