This paper proposes a new class of uniform continuous higher-order sliding mode algorithm (UCHOSMA) for the arbitrary relative degree systems. The proposed methodology is a combination of two controllers where one of the components is a uniform super-twisting control which acts as the disturbance compensator and the second part gives the uniform finite time convergence for the disturbance free system. This algorithm provides uniform finite time convergence of the output and its higher derivatives using an absolutely continuous control signal and thus alleviating the chattering phenomenon. The attractive feature of the proposed controller is that irrespective of the different initial conditions, the control is able to bring the states of the system to the equilibrium point uniformly in finite time. The effectiveness of the proposed controller has been demonstrated with both simulation and experimental results.