MicroRNAs are important modulators of gene expression. There is anecdotal evidence that the abundance of some microRNAs varies in circadian or approximately daily rhythm. In this study, using publicly available data we attempt a systematic analysis of co-expression between microRNAs and their prospective mRNA targets. An advanced analysis of periodicity with the application of digital filters in phase continuum revealed a baseline rhythmic oscillation on over 80% of both mRNA and microRNA populations. This computational observation adds evidence to the theory that microRNAs play an active role in modulation of rhythmic expression as a general rule rather than special exemption. We also explore the immediate implications of inferred oscillatory behavior for modeling of mRNA-miRNA dynamics.