In this paper, we look at an unique way of station keeping of a tethered satellite system. We design the boundary control based on the infinite dimensional model of the system dynamics. A linearized infinite dimensional system is obtained from the linearization of the nonlinear infinite dimensional system around the system relative equilibrium configuration. A boundary control is proposed for the stabilization of this linearized partial differential equation system and its stability analysis is performed using Lyapunov functions. Simulation results show the effectiveness of the proposed controller on the linear and non-linear systems. The proposed boundary controller does not constrain the tension in the tether to be positive