A differential-plunger device was used to measure the lifetimes of the lowest states in the πg7/2 ⊗ νh11/2 rotational band in doubly odd 112I with the 58Ni(58Ni, 3pn) reaction. A differential decay curve method was performed using the fully shifted and degraded γ -ray intensity measurements as a function of target-to-degrader distance. The lifetimes of the lowest three states in the πg7/2 ⊗ νh11/2 band in 112I were measured to be 124(30), 130(25), and 6.5(5) ps, respectively. As the lifetimes of successive excited states in a rotational band are expected to decrease with increasing excitation energy, these measurements suggest that the order of the transitions in the established band in 112I may need revising and that the state tentatively assigned to be (7−) may not belong to the rotational band.