The averaged profile of PSR 0329+54 shows a low degree of linear polarization across most of the pulse, and the position angle curve displays complicated variations which are highly inconsistent with the rotating vector model (RVM). Single-pulse polarization observations reported here demonstrate that these variations result from the coexistence throughout the profile of two orthogonal polarization modes with a complex, longitude-dependent frequency of occurrence. Each of these modes is well-described by the RVM. The presence of the two polarization modes explains not only the rapid orthogonal transitions but also the other complexities in the observed mean position angle curve. This model explains in very simple terms the bewildering complexity of one of the most studied pulsars. It is no longer necessary to invoke a second physical emission mechanism in order to explain the behaviour of this prototypical pulsar in the central part of the mean profile.