  Kerr-Schild metrics have been introduced as a linear superposition of the
flat spacetime metric and a squared null vector field, say $\boldsymbol{k}$,
multiplied by some scalar function, say $H$. The basic assumption which led to
Kerr solution was that $\boldsymbol{k}$ be both geodesic and shearfree. This
condition is relaxed here and Kerr-Schild ansatz is revised by treating
Kerr-Schild metrics as {\it exact linear perturbations} of Minkowski spacetime.
The scalar function $H$ is taken as the perturbing function, so that Einstein's
field equations are solved order by order in powers of $H$. It turns out that
the congruence must be geodesic and shearfree as a consequence of third and
second order equations, leading to an alternative derivation of Kerr solution.
