We have measured the ratio of the average sub-jet multiplicity in 3-jet to 2-jet events, R 23 , and 4-jet to 2-jet events, R 24 , using the e + e − annihilation data at s=58 GeV obtained from the AMY detector. We compare the measured values of R 23 and R 24 with the predictions of coherent and incoherent Monte Carlo models. R 23 is also compared with the NLLA calculations to all-orders. The color coherence effect has been observed to contribute to the suppression of R 23 and R 24 . Also, the difference of the behavior between gluon jets in 3-jet and 4-jet events has been studied.