Prominent in the 'Field of Streams' - the Sloan Digital Sky Survey map of substructure in the Galactic halo - is an 'Orphan Stream' without obvious progenitor. In this numerical study, we show a possible connection between the newly found dwarf satellite Ursa Major II (UMa II) and the Orphan Stream. We provide numerical simulations of the disruption of UMa II that match the observational data on the position, distance and morphology of the Orphan Stream. We predict the radial velocity of UMa II as - 100 km s-1, as well as the existence of strong velocity gradients along the Orphan Stream. The velocity dispersion of UMa II is expected to be high, though this can be caused both by a high dark matter content or by the presence of unbound stars in a disrupted remnant. However, the existence of a gradient in the mean radial velocity across UMa II provides a clear-cut distinction between these possibilities. The simulations support the idea that some of the anomalous, young halo globular clusters like Palomar 1 or Arp 2 or Ruprecht 106 may be physically associated with the Orphan Stream.