In the study of loops of Bol-Moufang types, a question that quickly comes to mind is this. Since a loop is an extra loop if and only if it is a Moufang loop and a CC-loop(or Cloop), then can one generalize this statement by identifying a "new identity" for a loop which generalizes the C-loop identity such that we can say "An Osborn loop is a Buchsteiner loop if and only if it obeys "certain" identity? A somewhat close answer to this question is the unpublished fact by M. K. Kinyon that "An Osborn loop Q with nucleus N is a Buchsteiner loop if and only if Q/N is a Boolean group" where Q/N being a Boolean group somewhat plays the role of the missing identity. It is proved that an Osborn loop is a Buchsteiner loop if and only if it satises the identity (x · xy)(x · xz) = x(x · yz). The importance of its emergence which was traced from the facts that Buchsteiner loops generalize extra loops while Osborn loops generalize Moufang loops is the fact that not every Osborn-Buchsteiner loop is an extra loop. An LC-loop obeys this identity. An Osborn-Buchsteiner loop (OBL) is shown to be nuclear square and to obey the identity x · xx = xx · x = x. Necessary and sucient condition for a OBL to be central square is established. It is shown that in an OBL, the cross inverse property and commutativity are equivalent, and the properties: 3-power associativity (xx · x = x · xx), self right inverse property (xx · x = x), self left inverse property (x · xx = x) and x = x are equivalent.