The frequency dependence of pulse width is studied for 150 normal pulsars, mostly selected from the European Pulsar Network, for which the 10\% multifrequency pulse widths can be well fit with the Thorsett relationship W_{10}=A\nu^{\mu}+W_{\rm 10, min}. The relative fraction of pulse width change between 0.4~GHz and 4.85~GHz, \eta=(W_{4.85}-W_{0.4})/W_{0.4}, is calculated in terms of the best-fit relationship for each pulsar. It is found that 81 pulsars (54\%) have $\eta<-10$\% (group A), showing considerable profile narrowing at high frequencies, 40 pulsars (27\%) have $-$10\%$\leq\eta\leq 10$\% (group B), meaning a marginal change in pulse width, and 29 pulsars (19\%) have $\eta>10$\% (group C), showing a remarkable profile broadening at high frequencies. The fractions of the group-A and group-C pulsars suggest that the profile narrowing phenomenon at high frequencies is more common than the profile broadening phenomenon, but a large fraction of the group-B and group-C pulsars (a total of 46\%) is also revealed. The group-C pulsars, together with a portion of group-B pulsars with a slight pulse broadening, can hardly be explained using the conventional radius-to-frequency mapping, which only applies to the profile narrowing phenomenon. Based on a recent version of the fan beam model, a type of broadband emission model, we propose that the diverse frequency dependence of pulse width is a consequence of different types of distribution of emission spectra across the emission region. The geometrical effect predicting a link between the emission beam shrinkage and the spectrum steepening is tested but disfavored.