We have studied the transport properties of a semiconductor quantum dot with steep walls in the Coulomb blockade regime and under strong magnetic fields with a filling factor between 2 and 4 inside the dot. A striking periodic suppression of Coulomb blockade resonances as a function of gate voltage is found, which reflects the selective coupling of dot states that belong to different Landau levels. The suppressed peaks are recovered under sufficiently high source-drain bias voltages and give rise to a novel type of structure superimposed on the Coulomb diamonds. The measurements are discussed in terms of both the charge density model, and the Fock-Darwin model. We argue that in order to explain the data, a non-parabolic confinement has to be assumed. We also find an alternating structure in the phase diagram and interpret this in terms of a spin effect.