We perform a detailed analysis of the migratory motion of human embryonic stem cells in two-dimensions, both when isolated and in close proximity to another cell, recorded with time-lapse microscopic imaging. We show that isolated cells tend to perform an unusual locally anisotropic walk, moving backwards and forwards along a preferred local direction correlated over a timescale of around 50 min and aligned with the axis of the cell elongation. Increasing elongation of the cell shape is associated with increased instantaneous migration speed. We also show that two cells in close proximity tend to move in the same direction, with the average separation of m or less and the correlation length of around 25 μm, a typical cell diameter. These results can be used as a basis for the mathematical modelling of the formation of clonal hESC colonies.