The tag-loss action response due to interaction with the set of four ultrafast pulses was recorded by the photodissociation yield at the MCP detector. Many background pathways coexist with the desired nonlinear signals. For instance, each pair of pulses contribute a linear signal and every set of three pulses generate a transient absorption background. In order to select desired 2D signals, we used phase cycling to remove unwanted signals. Each nonlinear pathway carries a phase dependence that is the linear combination of phases of each pulses in the pulse train. For rephasing and nonrephasing pathways, the phase dependencies are -φ1+φ2+φ3-φ4 and +φ1-φ2+φ3-φ4, respectively (φi is the phase of the i th pulse, the first pulse in time is φ1). The background linear pathway induced by the first and third pulses, for example, has a phase dependency of +φ1-φ3.