Boolean networks are used to model gene regulatory networks at a relatively high level. Finding Boolean networks with particular properties requires a representation that permits efficient search. In this study a novel representation for Boolean networks is implemented that segments the functioning of the network model that defines the network into discrete pieces. This design is intended to facilitate crossover-based retention of functionality in the networks, i.e. to make properties in an evolving population more heritable. The representation is tested on three different fitness functions and, on one of them, compared to the direct evolution of the entries of a matrix. The fitness function used to compare the novel and direct matrix representation demonstrates substantial superiority of the novel representation. The other two functions demonstrate the effectiveness of the new representation at a diversity of tasks. The representation, while useful for Boolean networks, has a number of potential applications to other domains.