While standing in the student parking lot directly east of McAllen High School in McAllen, Texas (Longitude: 98���14'13.94"W, Latitude 26���13'36.17"N), I was talking on my cell phone and happened to glance up at the sky. It was a bright, sunny, mostly clear day with hardly a cloud in the sky. I observed two bright, shiny "dots" flying in very close formation almost directly overhead but slightly west of my position. I can only describe them as "dots," seemingly circular in shape and very small in the sky from my vantage point. I could not tell if their bright appearance was due to reflection from the bright sun or an internal illumination.The objects were moving due west and, as they flew, they came very close together and then separated from each other several times (2 or 3 times). At one point, they seemed to almost touch, but then they separated, as they continued their track across the sky.Suddenly, both objects came to a complete stop in the sky and remained "frozen" for several moments before reversing their direction and heading back to the east. As they headed east, they began to appear smaller and more faint, which to me indicated that their altitude was increasing.I ran inside McAllen High School to get a friend of mine to come out and witness the objects, but he was not in his office. When I went back outside, the objects were so faint that they were barely visible. Moments later, when I finally contacted my friend, they were no longer visible.I have never had a "UFO sighting" in my life and was extremely shocked to observe what I observed. The fact that the two objects came to a complete stop in the sky for several moments and then reversed their direction indicates to me that these were not conventional aircraft.I am a computer specialist for the McAllen Independent School District and, due to the politics of my job, prefer to remain anonymous.