In order to describe partial cooperation structures, this paper introduces complete coalition 

systems as collections of feasible coalitions. A complete coalition system has the property that, 

for any coalition, if each pair of players in the coalition belongs to some feasible coalition 

contained in the coalition then the coalition itself is also feasible. The union stable systems, 

which constitute the domain of the Myerson value, are a special class of the complete coalition 

systems. As an allocation rule on complete coalition systems, this paper proposes an extension 

of the Myerson value and provides an axiomatization for it. The extended Myerson value 

coincides with the Myerson value over the union stable systems, but it also assigns payoff 

vectors to complete coalition systems which are not union stable systems. Thus, the extended 

Myerson value provides one method of more refined assignments of payoff vectors than the 

Myerson value.