  We investigate what we call a conformal $\beta $ - change in Finsler spaces,
namely $$ L(x,y)\to ~^{\ast}L(x,y)=e^{\sigma(x)}L(x,y)+\beta(x,y)$$
where~$\sigma ~$ is a function of $x~ only ~and ~ \beta (x, y)$ is a given 1-
form. This change generalizes various types of changes: conformal changes,
Randers changes and $\beta$ - changes. Under this change, we obtain the
relationships between some tensors associated with $(M,L)$ and the
corresponding tensors associated with $(M,{^\ast}L)$. We investigate some
$\sigma$- invariant tensors . This investigation allows us to give an answer to
the question: Are the properties of C-reducibility, $S_3$-likeness and
$S_4$-likeness invariant under a conformal $\beta$ - change?
