Observation datasets acquired by the Hyper Suprime-Cam (HSC) on the Subaru Telescope for the New Horizons mission target search were analyzed through a method that JAXA devised. This method has been used to detect fast-moving objects such as space debris or near-Earth asteroids, but we applied it to detect slow-moving objects such as trans-Neptunian objects (TNOs). In the New Horizons target search observations, we take continuous images of one field of view of the HSC for half a night, and this cadence fits the method well. The observations for the New Horizons Kuiper Belt Extended Mission using HSC began in May 2020, and are still ongoing. Here we show our result of the analysis of the dataset acquired from May 2020 through June 2021 that have already passed the proprietary period and are open to the public. We detected 84 TNO candidates in the June 2020 and June 2021 datasets, when the observation field was close to opposition. JAXA's detection method is different from that used by the New Horizons (NH) science team. Using JAXA's system, we found two new TNOs that were not on the list of TNOs detected by the NH science team.