Yes indeed - the variable being updated has to be situated outside of the function to be considered a closure.
The important aspect of a closure is that an outer function returns an inner function, with that returned inner function retaining knowledge of variables from the outer one.
The Jibbering Closures FAQ I still find to be highly insightful in regard to closures.
function exampleClosureForm(arg1, arg2){
var localVar = 8;
function exampleReturned(innerArg){
return ((arg1 + arg2)/(innerArg + localVar));
}
/* return a reference to the inner function defined as -
exampleReturned -:-
*/
return exampleReturned;
}
var globalVar = exampleClosureForm(2, 4);