My On Update Trigger Reacts Also On Delete

In SQL Server 2005 Express I created a trigger which should edit a value in another table when a special tupel column has been updated. The funny thing is, that it also fires on delete...of course not what I wanted. what did I do wrong?

Thanks in advance!

ALTER TRIGGER dbo.update_history_users

ON dbo.[user]

AFTER UPDATE

AS

IF UPDATE([name])

BEGIN

DECLARE @old_value nvarchar(MAX),

@new_value nvarchar(MAX);

SELECT @old_value = name FROM DELETED ;

SELECT @new_value = name FROM INSERTED ;

UPDATE dbo.history SET user_name = @new_value WHERE user_name = @old_value;

END