The total conversion coefficient of the 127.49 keV E3 isomeric transition in the decay of 134mCs was measured using the gamma intensity balance method with the help of a high resolution low energy photon detector. The er value was found to be 5.84_+0.47 as against the theoretical value of 6.96, thus showing an anomaly of (16.1 +6.7)%. The K-conversion coefficient, ~ was also measured using the X-ray peak to gamma ray intensity method and found to be 2.24+0.04 as against the theoretical value of 2.72, which shows an anomaly of (17.6_+ 1.4)% consistent with the experimental anomaly in at-The E 3 hindrance factor of the isomeric transition was estimated to be (3.44 _+ 0.23) 9 10 4.