The half-life for decay of 106In has been measured to be 5.3±0.1 min. A magnetic lens spectrometer was used to investigate the positon spectrum of this isotope. Two positon components were found whose transition energies are 4.89±0.03 and 2.7±0.1 MeV. Seven gamma rays involved in the decay of 106In have been resolved at energies of 0.53, 0.63, 0.86, 0.99, 1.66, 1.88 and 2.2 MeV. Beta-gamma coincidence measurements indicate the highest energy positon component to be coincident with only the 0.63 MeV gamma ray. In addition, the 2.7 MeV positon transition is coincident with gamma rays at 0.63, 0.86, 0.99, 1.66 and 1.88 MeV. The gamma rays at 0.63, 0.86 and 0.99 MeV were measured to be in coincidence. A search was made for the presence of an isometric state in the decay of 106In with a half-life in the range from 0.5 sec to several hours. The investigation produced no evidence for the existence of such a state.