An object is to provide a method of eliminating background amplification in detection of rare nucleic acids based on isothermal amplification. The method comprising steps of: preparing a mixture including solution and enzymes, and adding a first and a second template into the mixture, wherein the first template is an amplification template, and the second template is a leak absorption template. Methods to use this approach for multiplexed, ultrasensitive and ultra-specific detection of nucleic acids are presented.