This study investigates a new confidence criterion to improve fusion via a linear combination of scores of several biometric authentication systems. This confidence is based on the margin of making a decision, which answers the question, ``after observing the score of a given system, what is the confidence (or risk) associated to that given access?''. In the context of multimodal and intramodal fusion, such information proves valuable because the margin information can determine which of the systems should be given higher weights. Finally, we propose a linear discriminative framework to fuse the margin information with an existing global fusion function. This framework is simply a ``fusion of partial fusion'' because it directly modifies the weighing parameter of an existing fusion function. The results of 32 fusion experiments carried out on the XM2VTS multimodal database show that fusion using margin (product of margin and expert opinion) is superior over fusion without the margin information (i.e., the original expert opinion) . Furthermore, combining both sources of information increases fusion performance further.