  The energy of a graph is defined as the sum of the absolute values of all
eigenvalues of the graph. Akbari et al. \cite{S. Akbari} proved that for a
complete multipartite graph $K_{t_1 ,\ldots,t_k}$, if $t_i\geq 2 \
(i=1,\ldots,k)$, then deleting any edge will increase the energy. A natural
question is how the energy changes when $\min\{t_1 ,\ldots,t_k\}=1$. In this
paper, we will answer this question and completely determine how the energy of
a complete multipartite graph changes when one edge is removed.
