Summary: In some classification problems it may be important to impose constraints on the set of allowable solutions. In particular, in regional taxonomy, urban and regional studies often try to segment a set of territorial data in homogeneous groups with respect to a set of socio-economic variables taking into account, at the same time, contiguous neighbourhoods. The objects in a class are thus required not only to be similar to one another but also to be part of a spatially contiguous set. The rationale behind this is that if a spatially varying phenomenon influences the objects, as could occur in the case of geographical units, and this spatial information were ignored in constructing the classes then it would be less likely to be detected. In this paper a constrained version of the\(k\)-means clustering method and a new algorithm for devising such a procedure are proposed; the latter is based on the efficient algorithm proposed by J. A. Hartigan and M. A. Wong [J. R. Stat. Soc., Ser. C 28, 100–108 (1979; Zbl 0447.62062)]. This algorithm has proved its usefulness in zoning two large regions in Italy (Calabria and Puglia).