Alternating Sum of Volumes with Partitioning (ASVP) decomposition is a volumetric representation of a part obtained from its boundary representation that organizes faces of the part in an outside-in hierarchy. ASVP decomposition combines Alternating Sum of Volumes (ASV) decomposition, using convex hulls and set difference operations, and remedial partitioning, using cutting operations and concave edges. A Form Feature Decomposition (FFD) which can serve as a central feature representation for various applications is obtained from ASVP decomposition. The incremental update of convex decomposition is achieved by exploiting its hierarchical structure. For a connected incremental design change, the active components that only need to be updated are localized in a subtree of the decomposition tree called active subtree. Then, the new decomposition is obtained by only updating the active subtree in the old decomposition. In this paper, we present a new decomposition, called Augmented Alternating Sum of Volumes with Partitioning (AASVP) decomposition, that is incrementally constructed using ASV incremental update as a local operation on a decomposition tree. AASVP provides an improved feature recognition capability as it localizes the effect of the change in the decomposition tree, avoids excessive remedial partitioning and catches the designer’s intent in feature editing. AASVP differs from ASVP at the remedial-partitioning nodes by partitioning less. The current remedial partitioning method could be improved such that AASVP decomposition can be constructed directly from the solid model.