Many applications in mobile robotics require the safe execution of a real-time motion to a goal location through completely unknown environments. In this context, the dynamic window approach (DWA) is a well-known solution which is safe by construction —assuming reliable sensory information— and has shown to perform very efficiently in many experimental setups. Nevertheless, the approach is not free of shortcomings. Examples where DWA fails to attain the goal configuration due to the local minima problem can be easily found. This limitation, however, has been overcome by many researches following a common framework which essentially provides the strategy with a deliberative layer. Based on a model of the environment, the deliberative layer of these approaches computes the shortest collision-free path to the goal point being, afterwards, this path followed by DWA. In unknown environments, nevertheless, such a model is not initially available and has to be progressively built by means of the local information supplied by the robot sensors. Under these circumstances, the path obtained by the deliberative layer may repeatedly and radically change during navigation due to the model updates, which usually results in high-suboptimal final trajectories. This paper proposes an extension to DWA without the local minima problem that is able to produce reasonable good paths in unknown scenarios with a minimal computational cost. The convergence of the proposed strategy is proven from a geometric point of view.