The first results of studying the performance of a fast X-ray one-coordinate detector on the SR beam from VEPP-4 are presented. The detector consists of 128 independent channels, each being a scintillation counter on the basis of NaI(Tl) crystals. The spatial resolution of the detector constitutes 1.5 mm and its speed of response is 128 × 1 MHz. The main purpose of the detector is to examine the human circulatory system by the method of difference angiography at an energy of quanta corresponding to the K-absorption edge of iodine (33.2 keV). The first results on radiation exposure of the blood vessels of a live dog with a spatial resolution of 0.75 mm are given.