A new family of solutions describing the mean flow of an incompressible two‐dimensional wall jet subjected to boundary suction or blowing was found, in which the vertical velocity at the wall varies in a power law with downstream distance. Linear stability calculations indicate that two unstable modes, an inviscid inflectional point instability and a viscous instability, may coexist in the flow. It is demonstrated theoretically that the relative importance of each mode can be controlled by subjecting the wall jet to small amounts of blowing or suction. Experimental results, in the absence of suction and blowing, support theoretical findings about the coexistence of the two instability modes.