  We suggest a new method on coloring generalized Kneser graphs based on
hypergraphs with high discrepancy and small number of edges. The main result is
providing a proper coloring of K(n, n/2-t, s) in (4 + o(1))(s + t)^2 colors,
which is produced by Hadamard matrices. Also, we show that for colorings by
independent set of a natural type, this result is the best possible up to a
multiplicative constant. Our method extends to Kneser hypergraphs as well.
