  In this paper, we show that all odd-point correlation functions of the
balanced Rudin--Shapiro sequence vanish and that all even-point correlation
functions depend only on a single number, which holds for any weighted
correlation function as well. For the four-point correlation functions, we
provide a more detailed exposition which reveals some arithmetic structures and
symmetries. In particular, we show that one can obtain the autocorrelation
coefficients of its topological factor with maximal pure point spectrum among
them.
