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I was just thinking it would be nice watching an anime where the theme is suicide (death).

Something like "a character commits suicide (hopefully early in) and the other main characters revolve around this incidence"

As you might guess it would be a tragedy, and I hope I could get some advice from you guys.

Thanks for the advice, I've known about Lain for a while.

The only problem I see with that one is that "tragedy" isn't listed as a category so I was afraid it wasn't exactly what I was looking for.

I will gladly accept more advices if anyone knows about any other animes that might fit my description.

Hitsuji no Uta

I would recommend Kimi ga Nozomu Eien - Watch the relationship crumble as tragedy strikes! (It's not really suicide though)

Regards

Thanks, I'm downloading Hitsuji no Uta now.

Kimi ga Nozumo Eien is already on my to-see-list, but thanks for the notifier.