using a square tin in a small oven
First off, I personally love the hard edges of the brownie.
But to your question: 
    There are a few things that you can try to keep the edges from burning.


Use a lighter ( both color and heaviness ) pan, as this does affect the heating rate as well as the distribution of the heat throughout the pan. 
Try keeping your ingredients at a relative room temperature so there isn't a large transition from cold to hot in this oven ( the same reason you thaw some things before cooking ).
Try changing the temperature and cooking time. The recipes I usually stick with for brownies are cooking for about 30m at about 350 degrees F (175 c).


One last thing that might work that I have had to do with pie is wrapping foil around the edges until the last 10-15minutes of cooking.