Towards early detection of Alzheimer dementia (AD), this paper focuses on time-series instability of heart rate of AD patient, and proposes the AD detection method based on heart rate acquired by an unconstrained mattress sensor for daily life use. Through the human subject experiments on 124 days of heart rate of one AD patient and 39 days of heart rate of 21 healthy subjects, the following implication have been revealed: (1) an accuracy of the proposed AD detection method based on the time-series features of heart rate is approximately 98%; and (2) the time-series instability of heart rate is found in the rapid oscillation of heart rate (i.e., an increase/decrease of heart rate over 2 seconds).