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There does not exist an infinite sequence of 4-fold canonical flips. §1. Introduction One of the most important conjectures in the minimal model program is (log) Flip Conjecture II. It claims that any sequence of (log) flips: has to terminate after finitely many steps. In this paper, we prove it for 4dimensional canonical pairs. For the details of the log minimal model program, see [KMM, Introduction] or [KM, §3.7]. The following is the main theorem of this paper: Theorem 1.1 (Termination ofdoi:10.2977/prims/1145475971 fatcat:7xygziwhxnemtdiegsic7qxaje