The beta-delayed fission of 240Bk was studied following the reaction 241Am(3He,4n) at Elab=33 MeV. From the experiment the author obtains a half-life T12/=(4.2+or-0.8) min and a ground-state cross section of (28+or-16) mu b; using these data the beta-delayed fission probability is determined as (1.3-0.7+1.8)*10-5. The fission barrier parameters of 240Cm are obtained from an extrapolation of those for the adjacent 242Cm in accordance with the lifetimes. Assuming a Gaussian structure in the 240Bk beta strength function with a width of the order sigma =0.35 MeV, the centroid energy Ebeta =2.1+or-0.1 MeV is obtained from a model calculation. The model includes WKB resonant penetrability, double-delayed fission and microscopic level densities. Using published experimental data the fission barrier heights of 244,246,248Cf and 248,250Fm are estimated assuming the same strength functions. The consistency between the estimated barriers and known systematics is improved considerably with the inclusion of the strength function structure.