It is currently accepted that the dependences of frequency drift rate and instant duration of type III bursts on frequency follow a monotonic function. The observations carried out during summer months of 2002-2006 by the world largest decameter wavelength radio telescope UTR-2 in frequency band 10-30 MHz show that sometimes these dependences may have a jump at some frequency, when the steepness of the dependence changes step-wise. In this paper the results of observations of such unusual type III bursts are given. Since the dynamic spectrum of such bursts resembles a dog’s leg we call them “dog-leg” type III bursts. More than a hundred of these “dog-leg” bursts were observed during 5 years. The parameters of the 41 bursts observed in 2002 were defined and statistically analyzed. The fact that “dog-leg” type III bursts are observed on the background of standard type III bursts allows to exclude any instrumental component of the observed phenomena.