The sequential coalition formation model of Bloch to solve cooperative games with externalities exhibits some anomalies when related to classical concepts [Bloch, F., 1996. Sequential formation of coalitions in games with externalities and fixed payoff division. Games Econ. Behav. 14, 90-123]. We elaborate on these problems, define a modification of Bloch's model and show that its order-independent equilibria coincide with the (pessimistic) recursive core [Kóczy, L.Á., 2007. A recursive core for partition function form games. Theory Dec. 63, 41-51].