  We discuss the Fermion sign problem and, by examining a very general
Hubbard-Stratonovich (HS) transformation, argue that the sign problem cannot be
solved with such methods. We propose a different kind of transformation which,
while not solving the sign problem, shows more detailed information about the
system. With our transformation it is {\it trivial} to tell which auxiliary
field configurations give a positive sign and which give a negative sign. We
then discuss briefly various properties of this transformation and construct a
new algorithm which with one simulation gives results for a whole range of
particle densities and Hubbard $U$ values, positive and negative. Our approach
is in excellent agreement with exact calculations.
