  In this work we show a rational approximation of the Dawson's integral that
can be implemented for high-accuracy computation of the complex error function
in a rapid algorithm. Specifically, this approach provides accuracy exceeding
$\sim {10^{ - 14}}$ in the domain of practical importance $0 \le y < 0.1 \cap
\left| {x + iy} \right| \le 8$. A Matlab code for computation of the complex
error function with entire coverage of the complex plane is presented.
