The one-particle models of crystal-field theory provide a qualitative interpretation for the observed ground state splitting of four Kramers doublets of the S-8(7/2) of Bk4+ doped into CeF4. A set of nine nonzero (B-q(k)) parameters corresponding a C-2v point symmetry provide a very good correlation between the experimental data and simulated energy level schemes within a rms deviation of 13.7 cm(-1). The calculated and experimental energy values have the same order-of-magnitude for the ground state and excited components. The total ground state splitting of the S-state ions of f-elements such as Bk4+ in CeF4 is larger when compared with Cm3+:LaCl3 and Gd3+:La(C2H5SO4)(3). 9H(2)O ions. The so-called crystal-field strength parameter, N-v, increases as a function of the increasing maximum splitting of the ground state due to a decrease in the participation of the pure S-8(7/2) in the final composition of the ground state eigenvector. (C) 2000 American Institute of Physics. [S0021-9606(00)70509-5].