A method of manufacturing a radially anisotropic magnet, comprising the steps of furnishing a cylindrical magnet-compacting mold comprising a die having a cylindrical hollow interior, a cylindrical core disposed in the hollow interior to define a cylindrical cavity, and top and bottom punches disposed for vertical sliding motion within the cavity, packing a magnet powder in the cavity, applying a magnetic field across the magnet powder from outside the die and along a radial direction of the core, and forcing the top and bottom punches to compress the magnet powder for compacting the magnet powder by a horizontal magnetic field vertical compacting process, wherein the core of the magnet-compacting mold is composed at least in part of a ferromagnetic material with a saturation magnetic flux density of at least 0.5 T, the step of compacting the magnet powder packed in the mold cavity by a horizontal magnetic field vertical compacting process includes pre-compaction and thereafter, at least one of the following operation (i) to (iii): (i) subsequent to the magnetic field application, to rotate the magnet powder a given angle in the circumferential direction of the mold, then again apply a second magnetic field, (ii) subsequent to the magnetic field application, to rotate a magnetic field-generating coil a given angle in the circumferential direction of the mold relative to the magnet powder, then again apply a second magnetic field, and (iii) subsequent to the magnetic field application, to select a pair of coils shifted a given angle relative to the pair of coils which have been used for the magnetic field application, then again apply a second magnetic field therefrom, during or after application of the second magnetic field, or optionally after the pre-compaction and at least one of operations (i) to (iii) are repeated, the entire magnet powder is compressed under a pressure equal to or greater than that of partial compression by the entire top and bottom punches for finally compacting the magnet powder, characterised in that at least the top punch is divided into segments so that the magnet powder may be partially compressed in zones arcing an angle from ±10° to ±80° circumferentially from the magnetic field applying direction; and in the pre-compaction the magnet powder is partially compressed in zones arcing an angle from ±10° to ±80° circumferentially from the magnetic field applying direction during or after application of an orienting magnetic field across the magnet powder, by the segments of the top punch corresponding to the zones cooperating with the bottom punch for thereby consolidating the partially compressed zones of magnet powder to a density from 1.1 times the packing density prior to the magnetic field application to less than the compact ultimate density. (i) subsequent to the magnetic field application, to rotate the magnet powder a given angle in the circumferential direction of the mold, then again apply a second magnetic field, (ii) subsequent to the magnetic field application, to rotate a magnetic field-generating coil a given angle in the circumferential direction of the mold relative to the magnet powder, then again apply a second magnetic field, and (iii) subsequent to the magnetic field application, to select a pair of coils shifted a given angle relative to the pair of coils which have been used for the magnetic field application, then again apply a second magnetic field therefrom,