  We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a
Gaussian white noise and employ the dynamic renormalization-group of Yakhot and
Orszag without rescaling [J.~Sci.\ Comput.~{\bf 1}, 3 (1986)]. Hence we
calculate the second and third order moments of height distribution using the
diagrammatic method in the large scale and long time limits. The moments so
calculated lead to the value $S=0.3237$ for the skewness. This value is
comparable with numerical and experimental estimates.
