We present high-quality (subarcsecond) optical narrowband CCD images of the planetary nebula NGC 6881, which reveal a highly collimated bipolar structure. A careful examination of the [N II] image and of the [N II]/[O III] and [N II]/Hα ratio images shows that NGC 6881 is a quadrupolar planetary nebula, that is, a twice bipolar planetary nebula, each pair of lobes having a different symmetry axis. In addition, a striking knotty, looplike structure has been discovered in the southeast extreme of the nebula. Its appearance strongly suggests a precessing jetlike structure. Kinematical information of the different morphological features confirms the proposed nature of this nebula. The bright core is a ring that is collimating the bipolar lobes, while the looplike structure turns out to be a precessing jet. Assuming a simple ballistic model, an age of 7400d yr (d is the distance in kpc) is worked out, which can be compared with the computed age of the inner lobes of 400d yr. The precession period is 3800d yr. An upper limit of the ionized mass ejected (1.8 x 10^-5d^5/2 M_&sun;) in the precessing jet has also been calculated.