The splay orientational elastic constants for the nematic phases of a series of dimeric alpha,omega-bis(4-cyanobiphenyl-4-yloxy)alkanes have been determined by the method of Freedericksz threshold transitions in a magnetic field. A dramatic odd-even effect in the dependence of the elastic constant on the spacer length of the compounds investigated was revealed. It was shown that the splay elastic constant for the nematic dimers increases with increasing length of the molecules.