The continuity effect was investigated using frequency glides preceding and following a noise burst. First, the perceived trajectory of the glides during the noise was obtained by a method of drawing in which subjects were required to express what they had heard by drawing a line. The drawings showed that they did not simply interpolate the two frequency points at the beginning and end of the noise, but extrapolated the preceding glide through the noise. Second, two psychophysical experiments were conducted to examine the possibility of the frequency extrapolation. In the first experiment, subjects compared the duration of one glide with that of another followed by a noise. In the second experiment, they judged the final pitch of glide just before the noise. The results of both experiments showed that they traced the frequency change of the glide and perceived its extrapolated trajectory. The maximum duration of the extrapolation reached about 120 ms. This mechanism may underlie the continuity effect in general other than that with gliding tones, and is included in the cognitive model of auditory scene analysis proposed in another paper [Matsui et al., Proc. Spring Meet. Acoust. Soc. Jpn., pp. 485--486 (1996) (in Japanese)].