  Projection of many-body states with good angular momentum from an initial
state is usually accomplished by a three-dimensional integral. We show how
projection can instead be done by solving a straightforward system of linear
equations. We demonstrate the method and give sample applications to $^{48}$Cr
and $^{60}$Fe in the $pf$ shell. This new projection scheme, which is
competitive against the standard numerical quadrature, should also be
applicable to other quantum numbers such as isospin and particle number.
