  We report a new experimental scheme which combines atom interferometry with
Bloch oscillations to provide a new measurement of the ratio
$h/m_{\mathrm{Rb}}$. By using Bloch oscillations, we impart to the atoms up to
1600 recoil momenta and thus we improve the accuracy on the recoil velocity
measurement. The deduced value of $h/m_{\mathrm{Rb}}$ leads to a new
determination of the fine structure constant $\alpha^{-1}=137.035 999 45 (62)$
with a relative uncertainty of $4.6\times 10^{-9}$. The comparison of this
result with the value deduced from the measurement of the electron anomaly
provides the most stringent test of QED.
