Both 1→2 and 1→3 intersubband transitions have been observed in a step quantum well structure consisting of 60 A˚ GaAs wells, 90 A˚ Al0.18Ga0.82As steps, and 280 A˚ Al0.44Ga0.56As barriers. The transition energy and oscillator strength are 112 meV and 0.23 for the 1→2 transition and 150 meV and 0.15 for the 1→3 transition, respectively. The asymmetric property of a step quantum well allows the normally forbidden 1→3 transition to occur. The relaxation of the selection rule suggests a possibility of using optical pumping for infrared laser applications.