In this paper, we analyze the effect of the speed on the task of random number generation. Each subjectgenerates the sequences of ``random'' numbers under various speed conditions. In addition to the 16 indiceswhich have been used in the past studies, we introduce and calculate the new indices called the ``frequency ofschema''. From the statistical analysis, we find that there is an obvious change, along with the speed, in theproperties of sequences, indicating the transition of the underling information processing. It is shown that thefrequencies of schemas are effective indices for describing the properties of sequences produced under high-speed conditions.