Two types of cognitive tasks experiments, one through visual and the other through auditory presentation form were conducted to examine the correlation between eyeblinks and cognitive process, from the viewpoint of different nature of task phase. Blink rate and eyeblink intervals were analyzed statistically. As far as blink rate is concerned, by counting the number of eyeblinks based on the task phase, the index of blink rate to represent regularity of eyeblink occurrence was presented. Concerning eyeblink intervals, a new analysis approach using trend tests and correlation coefficients was verified. As trend tests for evaluations of statistical independence and underlying trend, reverse arrangement test in addition to conventional run test was applied to the obtained sequences of eyeblinks from the viewpoint of point process. Furthermore, under the guarantee of stationarity of an eyeblink sequence, correlation coefficients were calculated. The experimental results obtained by analysis of the above mentioned indices for eyeblink show that blink activity well synchronizes with the rhythm of the task phase.