The Fermi surfaces (FS) of LaOFeAs (in kz= 0 plane) consist of two hole-type circles around F point, which do not touch each other, and two electron-type co-centred ellipses around the M point, which are degenerate along the M - X line. By first-principles calculations, here we show that additional degeneracy exists for the two electron-type FS, and the crucial role ofF-doping and pressure is to enhance this orbital degeneracy. It is therefore suggested that the inter-orbital fluctuation is important to understand the unconventional superconductivity in these materials.