You could try saturating it with an oil based coat conditioner spray and then just pick it apart with a comb or your fingers. Start at the outside edges and seperate a few hairs at a time and hopefully you will work your way through the entire mat without having to cut anything off. If you don't have any coat conditioner you might use a human leave in conditioner.
Otherwise, if it's too big a matt you could split the matt with sissors. If possible slide the sissor blade between the matt and her skin (blade up away from her skin obviously) and gently saw your way up thru the matt. Do this a in a couple places until the matt is in smaller pieces (like dreadlocks) and you should be able to then brush it out. You will lose some hair this way but not as drastic as cutting off the whole matt and it should still look pretty good.
Good luck.
__________________ Dawn (Brandy & Titan's mom)  |