  We present a rational approximation for rapid and accurate computation of the
Voigt function, obtained by residue calculus. The computational test reveals
that with only $16$ summation terms this approximation provides average
accuracy ${10^{- 14}}$ over a wide domain of practical interest $0 < x <
40,000$ and ${10^{- 4}} < y < {10^2}$ for applications using the HITRAN
molecular spectroscopic database. The proposed rational approximation takes
less than half the computation time of that required by Weideman's rational
approximation. Algorithmic stability is achieved due to absence of the poles at
$y \geqslant 0$ and $ - \infty < x < \infty $.
