Continuous records of arterial blood pressure can be obtained non-invasively with Finapres, even for periods of 24 hours. Increasingly, storage of such records is done digitally, requiring large disc capacities. It is therefore necessary to find methods to store blood pressure waveforms in compressed form. The method of selection of significant points known from ECG data compression is adapted. Points are selected as significant wherever the first derivative of the pressure wave changes sign. As a second stage recursive partitioning is used to select additional points such that the difference between the selected points, linearly interpolated, and the original curve remains below a maximum. This method is tested on finger arterial pressure waveform epochs of 60 s duration taken from 32 patients with a wide range of blood pressures and heart rates. An average compression factor of 4.6 (SD 1.0) is obtained when accepting a maximum difference of 3 mmHg. The root mean squared error is 1 mmHg averaged over the group of patient waveforms. Clinically relevant parameters such as systolic, diastolic and mean pressure are reproduced with an offset error of less than 0.5 (0.3) mmHg and scatter less than 0.6 (0.1) mmHg. It is concluded that a substantial compression factor can be achieved with a simple and computationally fast algorithm and little deterioration in waveform quality and pressure level accuracy.