  We use a local model to study the formation and the structure of the low
energy charge transfer excitations in the insulating Cu-O$_2$ plane. The
elementary excitation is a bound exciton of spin singlet, consisting of a
Cu$^+$ and a neighboring spin singlet of Cu-O holes. The exciton can move
through the lattice freely without disturbing the antiferromagnetic spin
background, in contrast to the single hole motion. There are four eigen-modes
of excitons with different symmetry. The p-wave-like exciton has a large
dispersion width. The s-wave-like exciton mixes with p-state at finite
momentum, and its dipole transition intensity is strongly anisotropic. The
model is in excellent agreement with the electron energy loss spectra in the
insulating Sr$_2$CuO$_2$Cl$_2$.
