Yes. If I’m remembering well there are two Norton entries. Norton update and Norton antivir application. Check it please.
I have removed it every time when I have installed recovery image. At first I’ve removed Norton update and then Norton application. Everything went well and after notebook restart I’ve simply installed Avira antivir.
Anyway, as far as I know, Norton is just trial version and you can use it 60 days I think. So there must be some option where you can define your usage and this should not be shown anymore.