Ligation of the maxillary artery is a logical and effective method for the arrest of severe uncontrollable posterior epistaxis. The failure rates for arrest of haemorrhage are given in the literature as 10–13%. In our centre, over the last 9 years, 23 patients have undergone maxillary artery ligation to control epistaxis without a failure. Bilateral maxillary artery ligation was carried out whenever the maxillary artery of the bleeding side was found to be of small diameter. To investigate whether there is an asymmetry in the size of the maxillary arteries we performed 13 cadaveric dissections. In 6 of the cadavers one maxillary artery was significantly larger than the other. This fact has hitherto not been observed by otolaryngologists or anatomists. Failure to arrest haemorrhage may have resulted from ligation of the non‐dominant maxillary artery with consequent opening of cross‐anastamoses from the dominant