One of the long-standing problems in modern astronomy is the curious division of Galactic globular clusters, the "Oosterhoff dichotomy," according to the properties of their RR Lyrae stars. Here, we find that most of the lowest metallicity ([Fe/H] < -2.0) clusters, which are essential to an understanding of this phenomenon, display a planar alignment in the outer halo. This alignment, combined with evidence from kinematics and stellar population, indicates a captured origin from a satellite galaxy. We show that, together with the horizontal-branch evolutionary effect, the factor producing the dichotomy could be a small time gap between the cluster-formation epochs in the Milky Way and the satellite. The results oppose the traditional view that the metal-poorest clusters represent the indigenous and oldest population of the Galaxy.