All stars but one can be associated with an IAU (International Astronomical Union) constellation. IAU constellations are areas of the sky. Although there are only 88 IAU constellations, the sky is actually divided into 89 irregularly shaped boxes as the constellation Serpens is split into two separate sections, Serpens Caput (the snake's head) to the west and Serpens Cauda (the snake's tail) to the east.
The only star that does not belong to a constellation is the Sun. The Sun travels through the 13 constellations along the ecliptic, the 12 of the Zodiac and Ophiuchus.
Among the remaining stars, the nearer ones exhibit proper motion, so it is only a matter of time before some of them cross a constellation boundary and switch constellations as a consequence. In 1992, Rho Aquilae became the first star to have its Bayer designation "invalidated" by moving to a neighbouring constellation—it is now a star of the constellation Delphinus.[1]
Stars are listed in the appropriate lists for the constellation, as follows:
Constellation
Note that these lists are currently unfinished, and there may be stars missing that satisfy these conditions. If you come across one, please feel free to add it.