The difference of two negative integers is always negative.
If we subtract a smaller negative integer from the larger one, the answer will be a positive integer.
But when we subtract larger negative integer with smaller one, the answer will be a negative integer.
Let us take two examples:
Let and be two integers, then the difference between them will be
[Positive integer]
But when we subtract from , then
[Negative integer]
Thus, the difference of two negative numbers is not always negative.
Hence, the given statement is false.