York’s solution to the problem of linear least‐squares fits with errors in both coordinates [D. York, Can. J. Phys. 4 4, 1079 (1966)] is shown to be exact and not subject to the erroneous results that attempts to modify standard least‐squares algorithms can produce. Detailed examples of the use of York’s method are given; a fortran implementation suitable for use on personal computers is available to interested parties.