The paper presents an algorithm for reducing false alarms related to changes in arterial blood pressure (ABP) in intensive care unit (ICU) monitoring. The algorithm assesses the ABP signal quality, analyses the relationship between the electrocardiogram and ABP using a fuzzy logic approach and post-processes (accepts or rejects) ABP alarms produced by a commercial monitor. The algorithm was developed and evaluated using unrelated sets of data from the MIMIC database. By rejecting 98.2% (159 of 162) of the false ABP alarms produced by the monitor using the test set of data, the algorithm was able to reduce the false ABP alarm rate from 26.8% to 0.5% of ABP alarms, while accepting 99.8% (441 of 442) of true ABP alarms. The results show that the algorithm is effective and practical, and its use in future patient monitoring systems is feasible.