Unable to unlink Steam account from EA account

My EA account is currently  linked to an old Steam account that I no longer use. I would like to unlink this Stam account and connect a new Steam account instead. When I try to link the new one, I get the error message; "This EA account is already linked to another  Steam account."

Could you plase help me unlink the old Steam account or let me know if there is a way to change it?