Subject: Contradiction between Hawking radiation and second law of thermodynamics

Recently I learned that the entropy of a black hole is the black hole's surface 
area in disguise. Since according to the second law of thermodynamics, entropy 
must always increases, so a black hole's surface area must always increase as 
well. But according to the Hawking radiation, black hole can lose energy or 
mass, thus surface area as well, because of the negative energy density around 
it. So this means that entropy would decrease. Wouldn't that violate the second 
law of thermodynamics?

Re: Contradiction between Hawking radiation and second law of thermodynamics