  We present a method to accelerate the evaluation of the likelihood in
gravitational wave parameter estimation. Parameter estimation codes compute
likelihoods of similar waveforms, whose phases and amplitudes differ smoothly
with frequency. We exploit this by precomputing frequency-binned overlaps of
the best-fit waveform with the data. We show how these summary data can be used
to approximate the likelihood of any waveform that is sufficiently probable
within the required accuracy. We demonstrate that $\simeq 60$ bins suffice to
accurately compute likelihoods for strain data at a sampling rate of $4096\,$Hz
and duration of $T=2048\,$s around the binary neutron star merger GW170817.
Relative binning speeds up parameter estimation for frequency domain waveform
models by a factor of $\sim 10^4$ compared to naive matched filtering and $\sim
10$ compared to reduced order quadrature.
