The Self Organizing Map, or Kohonen SOM, is one of the most widely used neural network paradigm based on unsupervised competitive learning. However, the search algorithm introduced by Kohonen is slow when the size of the map is large. This slowness is caused by seeking about the best matching neuron among "all" the map neurons which tuned to "each" input sample. In this paper, we present a new strategy capable to accelerate the SOM's competition algorithm. Instead of Kohonen SOM strategy, the new approach concerns "only" with the neurons which are aligned along the low-order principal components of the feature space and neglects the rest of neurons. The idea is based on the fact that most of the data variance lie on the low-order principal components of the manifold which often contain the most important features of the data  . The new SOM can works effectively as a feature extractor for all kinds of manifolds even in the curved ones. Two data sets are utilized to illustrate how the proposed algorithm reduces the computation efforts (or time) of SOM effectively. For N-dimensions feature space, it is shown here that the computation effort to get the best matching units is reduced to O(D1+ D2+...+ DN) instead of O(D 1 × D2 × ... × DN), where Di is the number of neurons through the dimension i. Also, under same experimental conditions, our method computation time is less than that of fast DCT by sixth times. In all cases, the new SOM shows, at least, same recognition accuracy or may be better.