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For a simple graph $G$ on $n$ vertices and an integer $k$ with $1\le k\le n$, denote by ${𝒮}_k^{+}\left(G\right)$ the sum of $k$ largest signless Laplacian eigenvalues of $G$. It was conjectured that ${𝒮}_k^{+}\left(G\right)\le e\left(G\right)+\left(\genfrac{}{}{0pt}{}{k+1}{2}\right)$, where $e\left(G\right)$ is the number of edges of $G$. This conjecture has been proved to be true for all graphs when $k\in \{1,2,n-1,n\}$, and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all $k$). In this note, this conjecture is proved to be true for all graphs when $k=n-2$, and for some new classes of graphs.