  Let us consider a reference frame Sigma prime in which the pseudo-Euclidean
geometry holds. Einstein assumed that the principle of special relativity is
valid, i.e. the reference frame of any uniformly moving observer is also
described by the pseudo-Euclidean geometry. The transformation formulae from
one reference frame to the other one are therefore given by the well-known
Lorentz-transformations. But Einsteins assumption contradicts the observed
dipole anisotropy of the cosmic microwave background (CMB) in the universe. The
transformation formulae of the prefered reference frame Sigma prime in which
the pseudo-Euclidean geometry is valid to a uniformly moving observer in a
non-prefered reference frame Sigma are stated. The geomerty in Sigma is
anisotropic. The Doppler shift of objects moving in a non-prefered reference
frame is calculated. This result is applied to spacecrafts which fly near the
Earth. The observed anomalous frequency shift of several spacecrafts during
near Earth flybys does not arise in the non-prefered reference frame Sigma
