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This paper presents an iterative CKY parsing algorithm for probabilistic context-free grammars (PCFG). This algorithm enables us to prune unnecessary edges produced during parsing, which results in more efficient parsing. Since pruning is done by using the edge’s inside Viterbi probability and the upper-bound of the outside Viterbi probability, this algorithm guarantees to output the exact Viterbi parse, unlike beam-search or best-first strategies. Experimental results using the Penn Treebank II corpus show that the iterative CKY achieved more than 60% reduction of edges compared with the conventional CKY algorithm and the run-time overhead is very small. Our algorithm is general enough to incorporate a more sophisticated estimation function, which should lead to more efficient parsing.