Reiter's default logic can not handle inconsistencies and incoherences and thus is not satisfactory enough in commonsense reasoning. In the paper we propose a new variant of default logic named FDL in which the existence of extension is guaranteed and the trivial extension is avoided. Moreover, Reiter's default extensions are reserved and can be identified from the other extensions in FDL. Technically, we develop a paraconsistent and monotonic reasoning system based on resolution as the underlying logic of FDL. The definition of extension is also modified in the manner that conflicts between justifications of the used defaults and the conclusions of the extension, which we call justification conflicts, are permitted, so that justifications can not be denied by “subsequent” defaults and the existence of extension is guaranteed. Then we select the desired extensions as preferred ones according to the criteria that justification conflicts should be minimal.