  In this note, we study the maximum number $N_\alpha(d)$ of a system of
equiangular lines in $\mathbb{R}^d$ with cosine $\alpha$, where
$\frac{1}{\alpha}$ is not an odd positive integer. This note is motivated by a
remark in a $2018$ paper by Balla, Dr\"{a}xler, Keevash and Sudakov.
