The nonlinear refraction and nonlinear absorption phenomena are investigated in BaMgF(4) single crystal using the Z-scan technique in the ultraviolet region with a pulsed laser at 400 nm with 1 ps pulse duration. The remarkable nonlinear absorption behavior is identified to be three-photon absorption under the experimental conditions. In addition, both nonlinear refraction and nonlinear absorption have relatively large values and possess small anisotropy along three different crystallographic axes. The large values of nonlinear refractive index are demonstrated through the self-phase modulation effect.