
Let $f, g : (X, 0)\rightarrow (\mathbb{C}, 0)$ be germs of analytic functions defined over a complex analytic space $X$. The Brasselet number of a function $f$ describes numerically the topology of its generalized Milnor fibre. We study the local topology of a deformation of $g, \ \tilde{g}=g+f^N,$ for a positive integer number $N\gg1$ and provide a relation between the Brasselet number of $g$ and $\tilde{g}$ in $X\cap\{f=0\}$, in the case where $f$ has isolated singularity at the origin.