  The present paper deals with the Killing correspondence between some Finsler
spaces. We consider a Finsler space equipped with a $\beta$-change of metric
and study the Killing correspondence between the original Finsler space and the
Finsler space equipped with $\beta$-change of metric. We obtain necessary and
sufficient condition for a vector field Killing in the original Finsler space
to be Killing in the Finsler space equipped with $\beta$-change of metric.
Certain consequences of such result are also discussed.
