No.. Eliminating fats completely is rather unhealthy. Certain essential fatty acids actually help losing weight. So if you eliminate the fats from the diet and do nothing to restrict the amount of simple carbohydrates like refined sugar, refined flour, aerated drinks, etc. then the body will not let go off fat as simple sugars spike up the INSULIN levels in the body- a hormone which is also responsible for fat storage. Carbohydrates are the primary source of fuel to our body and the stored fat is the secondary source of fuel..so in the presence of adequate carbohydrates your body doesn't see any need to depend upon the body fats for energy, hence no fat loss takes place...