Is it ethical to TA in another university? My major field in undergraduate studies was A, whereas my current graduate field has been shifted to B (at a Canadian university).

I'm in trouble to find a TA position, as following:


At our department, B, faculty members prefer to choose the fellows, who had been in this field from their undergraduate studies. Because they themselves had passed these course within their studies, so are able to handle the case, more properly.
I'd just given a try for TA positions at department A (with which my background is compatible). Actually, the main source of funding at this department is TA. Therefore, the department does not accept unsolicited applications from the other departments for TA positions.


Furthermore, my tendency to catch at least one TA position stems from two things:


Funding,
Teaching experience.


Now, as I found that there is no potential chance at our university to hit the mark, I thought there might be some chances to be TA at adjacent universities. I realize that the same issues may be occurred about such cases, too. But, I'm wondering whether such attempt is ethical or not.

Any suggestion about resolving this problem is highly welcome.
Based on the other comments &amp; answer, there appears to be significant regional variation regarding this topic.

TAing in another university is certainly not uncommon eg. in Northern Europe, and in fact universities regularly cross-post TA advertisements to other universities, especially for lower-level courses that don't need special expertise and need a lot of TAs. 

There are generally not a lot of volunteer TAs. Based on the other answer, my guess is that this might have something to do with the lack of tuition fees in this area.