First, let's simplify the expression inside the parentheses:

(-1 3/7 + 5 3/7 - 4) = (4 3/7 + 5 3/7 - 4)
= 9 6/7 - 4
= 5 6/7

Now, let's multiply this result by -1 1/7:

5 6/7 -1 1/7 = -5 6/7 -1 1/7
= -5 -6/7 -1 -1/7
= -6 0/7 - 1/7
= -6 - 1/7
= -6 1/7

Therefore, (-1 3/7 + 5 3/7 - 4) * (-1 1/7) = -6 1/7.