We study analytically the moving nonlinear localized vibrational modes (dis
crete breathers) for a one-dimensional Klein-Gordon diatomic lattice in the
whole omega (q) plane of the system by means of a semi-discrete approximat
ion, in which the carrier wave of the modes is treated explicitly while the
envelope is described in the continuum approximation. We find that both pu
lse and kink envelope moving modes for this lattice system can occur with c
ertain carrier wave vectors and vibrational frequencies in separate regions
of the omega (q) plane. However, the kink envelope moving modes have not b
een reported previously for this lattice system.