This is the beauty of the low carb method. It is impossible to not burn fat. Think about why the fat is there. It is there to burn. Your body is not aware that civilisation has developed to the point where excess energy input is no longer required.
We are programmed to eat more than we need. Get over it

The body lays a fat store in the same way that hibernating bears do. They live off it over the winter. How? By not eating, but in particular, not eating energy sources.
Our will power is not sufficient for that. However, after you have used up all your blood sugar reserves, your body
will burn fat. It has no choice! I don't think there are any cases of fat people starving to death without going through a thin phase.
The point is your body will use less energy by burning your fat than it takes to digest and use any protein that you eat; and the protein stops the hunger pangs that always, always,
always make other diets fail. It's when you recognise that you are not dieting, but have made a lifestyle change in what you eat, that you succeed - and I made my change 2 years ago.
You
will need a small amount of carbs to "pump prime" the process, but it need only be about 30g daily.
You
will need to be rigorous; sendentary lifestyles need a very small amount of energy, and your body doesn't like to burn its hard-earned fat, so your metabolism slows down. This can be countered with exercise, if possible.
If you try it, remember that your body can use the energy in alcohol to avoid burning fat too (though it will not convert alcohol to fat).
This is old knowledge by the way, not Atkins. It's been around since the late 1700s.
See
http://en.wikipedia.org/wiki/Low-carbohydrate_diet but ignore the criticisms; Wiki authors tend to follow current liberal orthodoxies slavishly, including medical orthodoxies e.g. food pyramid.)