We trace the photospheric motions of 170 concentrations of magnetic flux tubes in and around the decaying active region No. 19824 (CMP 23 October 1986), using a series of magnetograms obtained at the Big Bear Solar Observatory. The magnetograms span an interval of just over five days and cover an area of about 4 × 5 arc min centered on the active region. We find a persistent large-scale flow pattern that is superposed on the small-scale random motions of both polarities. Correction for differential rotation unveils the systematic, large-scale flow surrounding the core region of the magnetic plage. The flow (with a mean velocity of 30 m s-1) is faster and more pronounced around the southern side of the core region than around the northern side, and it accelerates towards the western side of the active region. The northern and southern branches of the large-scale flow converge westward of the core region, dragging along the westernmost sunspot and some of the magnetic flux near it. The overall pattern of the large-scale flow resembles the flow of a river around a sand bar. The long-term evolution of the active region suggests that the flow persists for several months. We discuss the possible association of the large-scale flow with the torsional oscillation. We correct the observed motions of concentrations of flux tubes for the large-scale flow in order to study their random motions. The small-scale random motions (with a mean speed of 150 m s-1) can be characterized by a diffusion coefficient of ≃250 km2 s-1 for the area surrounding the core region of the magnetic plage. The diffusion coefficient characterizing the small-scale motions within the core region (mostly observed near its periphery and in areas of relatively low flux density) is only ≃ 110 km2 s-1. The lower diffusion coefficient in the core region appears to be caused mainly by a smaller step length rather than by a distinct difference in velocities.