Arterial blood pressure waveforms contain rich pathophysiological information; hence receive much attention in cardiovascular health monitoring. To assist computerized analysis, an automatic delineator was proposed for the fiducial points of arterial blood pressure waveforms, namely their onsets, systolic peaks and dicrotic notches. The presented delineator characterizes arterial blood pressure waveforms in a beat-by-beat manner. It firstly seeks the pairs of inflection and zero-crossing points, and then utilizes combinatorial amplitude and interval criteria to select the onset and systolic peak. Once a new beat is settled, the delineator seeks the derivative backward to locate the dicrotic notch in the preceding beat. In a nutshell, the delineator is based on the combinatorial analysis of arterial blood pressure waveforms and their derivatives. Three open databases, with an additional subset database, were utilized for delineator validation and performance evaluation. In terms of beat detection, the delineator achieved an average error rate 1.14%, sensitivity 99.43% and positive predictivity 99.45%. As to dicrotic notch detection, it performed well with an error rate 6.83%, sensitivity 96.53% and positive predictivity 96.64%.