The method of secret key sharing between units that did not possess any secret keys in advance is considered. It is assumed that between these units there are duplex wireless MIMO fading channels. In a recent paper published by D. Qin and Z. Dingh a new key sharing protocol has been proposed between legitimate users based on eigenvalues which are invariant under permutation of two matrices in their product. We extend this statement to a characteristic polynomial and by the way to matrix trace. Methods of key bits extraction are optimized both theoretically and experimentally. On the contrary to a statement of D. Qin and Z. Ding we prove that their key sharing protocol occurs insecure if eavesdroppers have the same channels as legitimate users. In order to provide reliability and security of the shared keys both error correction codes and privacy amplification methods can be used.