Taken inspiration from biological phenomenon that neurons communicate via spikes, spiking neural P systems (SN P systems, for short) are a class of distributed and parallel computing devices. So far firing rules in most of the SN P systems usually work in a sequential way or in an exhaustive way. Recently, a combination of the two ways mentioned above is considered in SN P systems. This new strategy of using rules, which is called a generalized way of using rules, is applicable for both firing rules and forgetting rules. In SN P systems with generalized use of rules (SNGR P systems, for short), if a rule is used at some step, it can be applied any possible number of times, nondeterministically chosen. In this work, the computational completeness of SNGR P systems is investigated. Specifically, a universal SNGR P system is constructed, where each neuron contains at most 5 rules, and for each time each firing rule consumes at most 6 spikes and each forgetting rule removes at most 4 spikes. This result makes an improvement regarding to these related parameters, thus provides an answer to the open problem mentioned in original work. Moreover, with this improvement we can use less resources (neurons and spikes involved in the evolution of system) to construct universal SNGR P systems.