  An oriented link projection is the image of a generic immersion of oriented
circles into the 2-sphere. The circle arrangement of a link projection is a
disjoint union of unoriented circles on the 2-sphere obtained by
orientation-incoherent smoothing at each crossing point. We show that two
oriented link projections have the same circle arrangement if and only if they
are transformed into each other by certain local moves. We also show that every
odd (resp. even) component link has a link projection whose circle arrangement
consists of exactly one (resp. two) circles.
