High resolution observations of the active region MacMath 16315 near the center of the disk were analysed in order to study the bright points, both below an Arch Filament system and in two neighbouring regions covered by plagettes. The average value of the relative intensity of the bright points with respect to the background in the plagette regions as well as under the Arch Filament system was 1.13 t 0.033. This value was the same for
Hα-1.0 A as well as for Hα-0.75 A . The lifetime of bright points under the Arch Filament System ranges from 3 to 18 min with
average value of 10 min. The time evolution of the intensity of bright points under the Arch Filament system is different from that of the Ellerman bombs under the same system f. The relative intensity of bright points rises to the maximum value within 1 min and remains constant during the rest of its lifetime. The average size of bright
points at Hα-1.0 A was found smaller than that at Hα-0.75 A.