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].