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We have already demonstrated the cutting of DNA at aimed position, which we named "molecular surgery", where DNA-cutting enzymes are immobilized on a micro particle, which is grasped by optical tweezers and pressed against stretch-and-positioned DNA, so that the cutting reaction occurs at the contact point. This paper for the first time demonstrates its reverse reaction, i.e. single molecule ligation, where two cohesive DNA ends are brought into close proximity by physical means under the presence of ligating enzymes, and joined together. The maximum extendable length after ligation is experimentally confirmed to be equal to the sum of the two DNA fragments joined. It is observed that the ligation seldom occurs when too long fragments are used, presumably due to the formation of randomly-coiled conformation which hampers the DNA ends from being well exposed for the interaction with the other fragment.