This paper presents a new method to generate a codebook that best represents the mapping between articulatory and acoustic domains. Existing codebook generation methods are relatively inefficient because of the non-linearities between the two domains. In our method the articulatory space is considered as composed of several hypercubes where the mapping is linear. The advantages of such a representation are the lower number of vectors which compose the codebook and the hierarchical organization of the codebook in a manner that respects the structure of the two domains.