  We present a covariant formalism for general multi-field system which enables
us to obtain higher order action of cosmological perturbations easily and
systematically. The effects of the field space geometry, described by the
Riemann curvature tensor of the field space, are naturally incorporated. We
explicitly calculate up to the cubic order action which is necessary to
estimate non-Gaussianity and present those geometric terms which have not yet
known before.
