  In this paper, a technique on constructing nonlinear resilient Boolean
functions is described. By using several sets of disjoint spectra functions on
a small number of variables, an almost optimal resilient function on a large
even number of variables can be constructed. It is shown that given any $m$,
one can construct infinitely many $n$-variable ($n$ even), $m$-resilient
functions with nonlinearity $>2^{n-1}-2^{n/2}$. A large class of highly
nonlinear resilient functions which were not known are obtained. Then one
method to optimize the degree of the constructed functions is proposed. Last,
an improved version of the main construction is given.
