Almost all cells display circadian rhythms, approximately 24-hour period changes in their biochemistry, physiology or behavior. These rhythms are orchestrated by an endogenous circadian clock whose mechanism is based on transcription-translation feedback loops (TTFL) where the translated products of clock genes act to inhibit their own transcription. We have used RNA-Seq to measure the abundance of all transcripts in an RNA-Seq-derived de novo gene catalog in two different experiments. One compared midday and midnight in a light–dark cycle (ZT6 and ZT18) and under constant light (CT6 and CT18). The second compared four different times (ZT2, ZT6, ZT14 and ZT18) under a light dark cycle. We show here that despite an elaborate repertoire of biological rhythms, the unicellular dinoflagellate Lingulodinium had no detectable daily variation in the abundance of any transcript in an RNA-Seq-derived de novo gene catalog. We also examined the timing of the bioluminescence and photosynthesis rhythms in the presence of the transcription inhibitors actinomycin D and cordycepin. We found that the timing of the two rhythms was unchanged even when transcription rates had decreased to roughly 5% the levels of untreated cells. The lack of detectable daily variation in transcript levels indicates that the endogenous circadian timer of Lingulodinium does not require rhythmic RNA. If the circadian timer is considered as a limit cycle oscillator, then cellular time in this organism must be defined by variations in state variables that do not include the amount of a clock gene transcript.