  We identify a large class of one-loop amplitudes for massless particles that
can be constructed via unitarity from tree amplitudes, without any ambiguities.
One-loop amplitudes for massless supersymmetric gauge theories fall into this
class; in addition, many non-supersymmetric amplitudes can be rearranged to
take advantage of the result. As applications, we construct the one-loop
amplitudes for $n$-gluon scattering in $N=1$ supersymmetric theories with the
helicity configuration of the Parke-Taylor tree amplitudes, and for six-gluon
scattering in $N=4$ super-Yang-Mills theory for all helicity configurations.
