In the context of the Instituto de Astrofisica de Canarias (IAC) morphological survey of Galactic planetary nebulae (PNs), a new morphological class has been found, and we define their members as quadrupolar PNs. We have found five quadrupolar objects whose lobes are, in pairs, symmetric with respect to two different axes. Among these PNs, three (M2-46, K3-24, and M1-75) have well-defined pairs of lobes; another two (M3-28 and M4-14) are irregular and very possibly quadrupolar. For M2-46, we have measured the extension and the angle between the lobes, and the expansion velocities of the lobes by means of spectroscopic analysis. We propose that these nebulae have been formed by precession of the rotation axis of the central stars, possibly in the presence of a binary companion, associated with multiple shell ejection at the asymptotic giant branch. A simple binary mechanism not associated with precession cannot produce such a morphology.