Network meta-analysis (NMA) can be used to compare multiple competing treatments for the same disease. In practice, usually a range of outcomes is of interest. As the number of outcomes increases, summarizing results from multiple NMAs becomes a nontrivial task, especially for larger networks. Moreover, NMAs provide results in terms of relative effect measures that can be difficult to interpret and apply in every-day clinical practice, such as the odds ratios. In this article, we aim to facilitate the clinical decision-making process by proposing a new graphical tool, the Kilim plot, for presenting results from NMA on multiple outcomes. Our plot compactly summarizes results on all treatments and all outcomes; it provides information regarding the strength of the statistical evidence of treatment effects, while it illustrates absolute, rather than relative, effects of interventions. Moreover, it can be easily modified to include considerations regarding clinically important effects. To showcase our method, we use data from a network of studies in antidepressants. All analyses are performed in R and we provide the source code needed to produce the Kilim plot, as well as an interactive web application.