We present the Self-Loop Aggregation Product (SLAP), a new hybrid technique that replaces the synchronized product used in the automata-theoretic approach for LTL model checking. The proposed product is an explicit graph of aggregates (symbolic sets of states) that can be interpreted as a Büchi automaton. The criterion used by SLAP to aggregate states from the Kripke structure is based on the analysis of self-loops that occur in the Büchi automaton expressing the property to verify. Our hybrid approach allows on the one hand to use classical emptiness-check algorithms and build the graph on-the-fly, and on the other hand, to have a compact encoding of the state space thanks to the symbolic representation of the aggregates. Our experiments show that this technique often outperforms other existing (hybrid or fully symbolic) approaches.