A new programmable neighborhood mechanism for the Winner Takes Most (WTM) self-organizing Kohonen map has been proposed in this paper. Described circuit is an asynchronous solution, which does not require the controlling clock generator. The winning neuron generates the `enable’ signal (EN) that spreads in all directions in the map, triggering adaptation process in all neurons that belong to the winner’s neighborhood. Time propagation of the EN signal is very short. In an example map that consists of 32x32 neurons, the propagation time between two neurons that are the most distant is equal to about 60 ns, which in practice means that adaptation in all neurons starts almost in the same time and is then performed in parallel. The proposed solution makes any hardware implemented WTM network almost as fast as the Winner Takes All (WTA) network, which does not contain the neighborhood mechanism and allows for adaptation only of the winning neuron in each of iterations.