Inteins are single turnover enzymes that splice out of protein precursors during maturation of the host protein (extein). The Cys or Ser at the N terminus of most inteins initiates a four-step protein splicing reaction by forming a (thio)ester bond at the N-terminal splice junction. Several recently identified inteins cannot perform this acyl rearrangement because they do not begin with Cys, Thr, or Ser. This study analyzes one of these, the mycobacteriophage Bethlehem DnaB intein, which we describe here as the prototype for a new class of inteins based on sequence comparisons, reactivity, and mechanism. These Class 3 inteins are characterized by a non-nucleophilic N-terminal residue that co-varies with a non-contiguous Trp, Cys, Thr triplet (WCT) and a Thr or Ser as the first C-extein residue. Several mechanistic differences were observed when compared with standard inteins or previously studied atypical KlbA Ala(1) inteins: (a) cleavage at the N-terminal splice junction in the absence of all standard N- and C-terminal splice junction nucleophiles, (b) activation of the N-terminal splice junction by a variant Block B motif that includes the WCT triplet Trp, (c) decay of the branched intermediate by thiols or Cys despite an ester linkage at the C-extein branch point, and (d) an absolute requirement for the WCT triplet Block F Cys. Based on biochemical data and confirmed by molecular modeling, we propose roles for these newly identified conserved residues, a novel protein splicing mechanism that includes a second branched intermediate, and an intein classification with three mechanistic categories.