According to the medical research report that the melatonin secretion of Alzheimer dementia (AD) patients shows the circadian rhythm (approximately 24 hours) disorder, this paper proposes the AD detection method based on circadian rhythm disorder of heartrate. The proposed method based on the regression of the trigonometric functions with the maximum likelihood estimation computes the ratio between the circadian rhythm of the heartrate and its non-circadian rhythm, to judge that the circadian rhythm is strong or weak, and detects AD in order with two types of the circadian ratios, the first circadian rhythm ratio based on the absolute mean of circadian/non-circadian rhythm and the second circadian rhythm ratio based on the diurnal amplitude of estimated heart rate. The analysis of the human subject experiment, with one elderly AD patient, three elderly (60-70 generations) non-AD persons, the ten middle-aged persons and the eight young persons, revealed the following implications: (1) the first circadian rhythm ratio judged 100.0% of AD,83.3% of the elderly, 28.6% of the middle-aged and 20.0% of the young as weak circadian (i.e., separated AD patients and the elderly from the middle-aged and young); (2) and, with the judgement by the first ratio, the second circadian rhythm ratio judged and finally detected 91.7% of AD,16.7% of the elderly, 7.1% of the middle-aged and 0.0% of the young as weak circadian and AD (i.e., separated AD patients and the elderly).