  We consider binary systems of coalescing, nonspinning, black holes of masses
$m_{1}$ and $m_{2}$ and show that the gravitational recoil velocity for any
mass ratio can be obtained accurately by extrapolating the waveform of the
test-mass limit case. The waveform obtained in the limit $m_1/m_2\ll 1$ via a
perturbative approach is extrapolated in $\nu= m_{1} m_{2}/(m_{1}+m_{2})^{2} $
multipole by multipole using the corresponding, analytically known,
leading-in-$\nu$ behavior. The final kick velocity computed from this
$\nu$-flexed waveform is written as $v(\nu)/c = 0.04457
\nu^2\sqrt{1-4\nu}\,(1-2.07106\nu + 3.93472\nu^2 -4.78404\nu^3+2.52040\nu^{4})$
and is compatible with the outcome of numerical relativity simulations
