When people want to exchange digital money and digital data over the Internet like a market, privacy for the participant’s behavior, security against malicious users and fair- ness for matching must be assured. We propose a new concept “Matching Oblivious Transfer,” which can match valuable digital data with hiding the price suggested by participant and securely deliver the digital data to the matched participant. Then we pro- pose a protocol for some general matching rules in which once a participant sends an order to the market, no interaction between each participant and the market is needed.