The straightness of a digital arc can simply be determined by the absence of unevenness in its chain code. The absence of unevenness is a necessary and sufficient condition for a digital arc to have the chord property, and it offers a much simpler alternative for examining whether a digital arc has the chord property or not. This condition is also the most comprehensive and precise expression of the third criterion about digital straight lines given by Freeman. The relations among the chord property, Freeman's three criteria, and the hierarchical structure that a digital straight line supposedly have become much more clear. A procedure to detect the uneven segments and algorithms for determining the straightness of digital arcs is also included.