  In planar N=4 SYM we study a particular class of helicity preserving
amplitudes. These are scalar amplitudes whose flavor configuration is chosen in
such a way that only a limited number of diagrams is allowed, which exhibit an
iterative structure. For such amplitudes we evaluate the tree level and
one-loop contributions, providing a general formula valid for any number of
particles. The ratio between the one-loop and tree level results is a simple
combination of dual conformally invariant box functions with at most two
massive legs. Along with the MHV and NMHV series, this constitutes the third
known infinite sequence of one-loop amplitudes in N=4 SYM.
