A transition duct for use in a turbine engine is provided. The transition duct includes a radially inner wall and a radially outer wall positioned about the radially inner wall defining a flow passage therebetween. The radially outer wall extends and is contoured from an upstream end to a downstream end of the transition duct. As such, the slope of the radially outer wall increases from the upstream end to a predetermined axial location and decreases from the predetermined axial location to the downstream end.