  We present a simple method to track the precession of a black-hole-binary
system, using only information from the gravitational-wave (GW) signal. Our
method consists of locating the frame from which the magnitude of the
$(\ell=2,|m|=2)$ modes is maximized, which we denote the "quadrupole-aligned"
frame. We demonstrate the efficacy of this method when applied to waveforms
from numerical simulations. In the test case of an equal-mass nonspinning
binary, our method locates the direction of the orbital angular momentum to
within $(\Delta \theta, \Delta \phi) = (0.05^{\circ},0.2^{\circ})$. We then
apply the method to a $q = M_2/M_1 = 3$ binary that exhibits significant
precession. In general a spinning binary's orbital angular momentum
$\mathbf{L}$ is \emph{not} orthogonal to the orbital plane. Evidence that our
method locates the direction of $\mathbf{L}$ rather than the normal of the
orbital plane is provided by comparison with post-Newtonian (PN) results. Also,
we observe that it accurately reproduces similar higher-mode amplitudes to a
comparable non-spinning (and therefore non-precessing) binary, and that the
frequency of the $(\ell=2,|m|=2)$ modes is consistent with the "total
frequency" of the binary's motion. The simple form of the quadrupole-aligned
waveform will be useful in attempts to analytically model the
inspiral-merger-ringdown (IMR) signal of precessing binaries, and in
standardizing the representation of waveforms for studies of accuracy and
consistency of source modelling efforts, both numerical and analytical.
