How to keep count in a recursive function?

I wrote a recursive function to find the number of instances of a substring in the parent string.

The way I am keeping count is by declaring/initialising count as a global variable outside the function's scope. Problem is, it'll give me correct results only the first time the function is run, because after that count != 0 to begin with. And if i have it inside the function, than each time it is called recursively, it'll be set to 0.

count=0
def countSubStringMatchRecursive(target,key):
    index=find(target,key)
    global count
    targetstring=target
    if index>=0:
        count=count+1
        target=target[index+len(key):]
        countSubStringMatchRecursive(target,key)
    else :
        pass
    return "No. of instances of", key, 'in', targetstring, 'is', count

Note: I am looking for the solution for a recursive function specifically, I have an iterative function that does work fine.

EDIT: Thank You all, this was part of homework, so I was only using the string module