Intensity maxima and zeros of speckle patterns obtained behind a diffuser are experimentally interchanged by applying a spiral phase delay of charge ±1 to the impinging coherent beam. This transform arises from the expectation that tightly focused beams, which have a planar wave front around the focus, are so changed into vortex beams and vice versa. The statistics of extrema locations and the intensity distribution of the so-generated "complementary" patterns are characterized by numerical simulations. It is demonstrated experimentally that the incoherent superposition of the three "complementary speckle patterns" yield a synthetic speckle grain size enlarged by a factor of sqrt. A cyclic permutation of optical vortices and intensity maxima is unexpectedly observed and discussed.