Quick answer, yes. Cut it off as close to the live branch as possible without damaging the new growth.

thank you very much.

would i be right thinking this is a salix nishiki but the top had died, It looks to me like it has sprouted from the original host, as nishiki is grafted onto the top of it, so i would be tempted to remove it all if that is the case as you may end up with a very large salix.

Then again i might be wrong..

It looks like a grafted tree where the graft has died and the rootstock has taken over to me. Is the branch that's alive EXACTLY as it should be?

I agree teh graft has died and the rootstock has taken over - remove unless you want a large salix!

i agree its just going to be a big willow near your house

Thank you for all your replies. So are you all saying that should remove the dead part of the tree then?

could someone explain to me what is a grafted tree is please?

thank you for your help, :-)

Berryboo you need to remove the whole tree. A grafted tree is one where they take a good rootstock and graft a scion (woody branch) from the same family but a different species onto it. If the scion dies which is what has happened with your tree the rootstock takes over and grows. In this case that would result in you having a very large common willow growing near your house. Dig it out now whilst you can.

Take a look at this website http://www.extension.umn.edu/distribution/horticulture/dg0532.html
the info is for grafting fruit trees but the method is the same.

Now I would have said that the graft union was further down the tree stem than where the dead branch is, but then my eyesight is not getting any better. And if you like the tree then keep it and pollard or coppice it. We have a potentially large willow which we cut back to the stump every other year. It keeps it small and looking good.

this plant or tree has the graft righte at the top though lots are at the bottem .if you look closley at the top you can see the graft.