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Radio-occultation (RO) technique, which has been used in planetary science, is a method to obtain the profiles of atmosphere and the global atmospheric data. In 2006, Taiwan launched six low-Earth-orbit satellites as a RO constellation mission, known as FORMOSAT-3. In order to thoroughly understand the process of the RO data retrieval and obtain as much as possible the information for the weather prediction, a National Central University Radio Occultation (NCURO) retrieval algorithm has been developed. The focus of the algorithm development is on the correction of the excess phase of the signal received with open-loop (OL) technique and the criteria for assessment of the data quality. When the OL is activated, the excess phase of the Global Positioning System (GPS) signal is modulated with navigation messages of satellites. In our algorithms, two methods are incorporated to recover the excess phase. Moreover, as the altitude of the received signal decreases, the quality of the GPS signal generally deteriorates, and eventually, the signal is too noisy to be processed. In order to assess the quality of the signal, instead of the signal-to-noise ratio, the degree of unclearness is defined and used in the algorithm. In this paper, the algorithm including the phase-correction methods and the criteria for the quality assessment will be described. The data retrieval using the algorithm will be compared with those obtained from the COSMIC Data Analysis and Archive Center at the University Corporation for Atmosphere Research and Pingtung radiosonde measurement. Some intermediate results of the NCURO algorithm will also be demonstrated.