An all fiber reflected Mach Zehnder interferometer was studied in details with the interference method for the first time to our knowledge.The energy transmission matrix of the interferometer was deducted.The relationships between the splitting ratios of the couplers,the length difference of two arms and the intensity transmission spectrum were obtained.When k=0.5,the interference pattern fringe period for a reflected Mach Zehnder interferometer is half of that of a transmitted Mach Zehnder interferometer.The relationship between the wavelength difference of two adjacent transmission peaks and the difference of two arms was also discussed.