  Co$_{4}$B$_{6}$O$_{13}$ contains undistorted tetrahedral clusters of magnetic
Co$^{2+}$ ions. The high-field magnetization of this magnet exhibits a periodic
undulation indicating quantization of the total spin number per cluster.
Measurements of magnetic susceptibility and specific heat reveal that the
ground state is composed of several different singlet states, reflecting the
high symmetry of the spin tetrahedron. An exact diagonalization calculation
taking account of single-ion type anisotropies and Dzyaloshinsky-Moriya
interactions reproduces the expretimental results very well.
