Hydrodynamical calculations in three space dimensions of the collapse of an isothermal, centrally condensed, rotating 1-M_ protostellar cloud are presented. A numerical algorithm involving nested subgrids is used to resolve the region where fragmentation occurs in the central part of the protostar. A previous calculation by Boss, which produced a hierarchical multiple system, is evolved further, at comparable numerical resolution, and the end result is a binary, with more than half of the mass of the original cloud, plus a central object formed from the merger of small inner fragments. The orbital separation of the main binary increases with time as a result of accretion of high-angular-momentum material, and as a result of merging with fragments that have formed farther out. Repeating the calculation with significantly higher resolution, we find that a sequence of binaries can be induced by fragmentation of circumbinary discs. The stability of the resulting multiple system is investigated using n-body calculations, which indicate that such a system would transform on a short time-scale into a more stable hierarchical structure. The outermost and most massive binary which forms in the high-resolution run has properties similar to that of the binary found in the low-resolution calculation. Thus the basic outcome is shown to be independent of the numerical spatial resolution. The high-resolution run, in addition, leads to the formation of an inner system of smaller fragments, which might be important for the understanding of the origin of close binaries with low-mass components and of low-mass single stars.