In routine clinical practice the variations of the radial artery are the main reason for technical failure during transradial catheterization. If these variations are well documented, however, they do not represent a problem in the transradial approach. Therefore, we report here a rare case of the radial artery which is very strange but potentially valuable for the clinical practice: it arises at a right angle from the brachial artery and passes behind the biceps brachii tendon. Based on our findings and on an extensive literature review, we propose for the first time a clinically oriented classification of the variations of the radial artery. This classification is related to the catheterization success at the usual access site of the radial artery at the wrist.