  Scalar field models of inflation based on a large nonminimal coupling to
gravity xi, in particular, Higgs inflation, may violate unitarity at an energy
scale ~ M_p / xi << M_p. In this case the model is incomplete at energy scales
relevant to inflation. Here we propose a new unitarity-conserving model of
Higgs inflation. The completion of the theory is achieved via additional
interactions which are proportional to products of the derivatives of the Higgs
doublet. The resulting model differs from the original version of Higgs
inflation in its prediction for the spectral index, with a classical value n =
0.974. In the case of a nonsupersymmetric model, quantum corrections are likely
to strongly modify the tree-level potential, suggesting that supersymmetry or a
gauge singlet scalar inflaton is necessary for a completely successful model.
