Dissolved gas analysis (DGA) is one of the most useful techniques to detect incipient faults in power transformers. However, the identification of the faulted location by the traditional method is not always an easy task due to the variability of gas data and operational variables. In this paper, a novel extension method is presented for fault diagnosis of power transformers, which is based on the matter-element model and extended relation functions. Thus, incipient faults in power transformers can be directly identified by the degree of relation. The application of this new method to some transformers has yielded promising results.