On the sum of normal matrices

This short paper revisits a remarkable but almost overlooked result of Djokovi\'{c} [Proc. Amer. Math. Soc. 27 (1971) 19-23]. A connection to a result of \u{S}emrl is pointed out. With Djokovi\'{c}'s result, an extension of Craig-Sakamoto theorem to $k$ ($k\ge 2$) normal matrices is presented. A comment to a recent monthly problem is also given.