We have carried out observations of CCH and its two ^ { 13 } C isotopologues , ^ { 13 } CCH and C ^ { 13 } CH , in the 84 – 88 GHz band toward two starless cores , L1521B and L134N ( L183 ) , using the Nobeyama 45 m radio telescope . We have detected C ^ { 13 } CH with a signal-to-noise ( S/N ) ratio of 4 , whereas no line of ^ { 13 } CCH was detected in either the dark clouds . The column densities of the normal species were derived to be ( 1.66 \pm 0.18 ) \times 10 ^ { 14 } cm ^ { -2 } and ( 7.3 \pm 0.9 ) \times 10 ^ { 13 } cm ^ { -2 } ( 1 \sigma ) in L1521B and L134N , respectively . The column density ratios of N ( C ^ { 13 } CH ) / N ( ^ { 13 } CCH ) were calculated to be > 1.1 and > 1.4 in L1521B and L134N , respectively . The characteristic that ^ { 13 } CCH is less abundant than C ^ { 13 } CH is likely common for dark clouds . Moreover , we find that the ^ { 12 } C/ ^ { 13 } C ratios of CCH are much higher than those of HC _ { 3 } N in L1521B by more than a factor of 2 , as well as in Taurus Molecular Cloud-1 ( TMC-1 ) . In L134N , the differences in the ^ { 12 } C/ ^ { 13 } C ratios between CCH and HC _ { 3 } N seem to be smaller than those in L1521B and TMC-1 . We discuss the origins of the ^ { 13 } C isotopic fractionation of CCH and investigate possible routes that cause the significantly high ^ { 12 } C/ ^ { 13 } C ratio of CCH especially in young dark clouds , with the help of chemical simulations . The high ^ { 12 } C/ ^ { 13 } C ratios of CCH seem to be caused by reactions between hydrocarbons ( e.g. , CCH , C _ { 2 } H _ { 2 } , l,c -C _ { 3 } H ) and C ^ { + } .