The idea that memories are immutable after consolidation has been challenged. Several reports have shown that after the presentation of a specific reminder, reactivated old memories become labile and again susceptible to amnesic agents. Such vulnerability diminishes with the progress of time and implies a re-stabilization phase, usually referred to as reconsolidation. To date, the main findings describe the mechanisms associated with the labilization-reconsolidation process, but little is known about its functionality from a biological standpoint. Indeed, two functions have been proposed. One suggests that destabilization of the original memory after the reminder allows the integration of new information into the background of the original memory (memory updating), and the other suggests that the labilization-reconsolidation process strengthens the original memory (memory strengthening). We have previously reported the reconsolidation of human declarative memories, demonstrating memory updating in the framework of reconsolidation. Here we deal with the strengthening function attributed to the reconsolidation process. We triggered labilization-reconsolidation processes successively by repeated presentations of the proper reminder. Participants learned an association between five cue-syllables and their respective response-syllables. Twenty-four hours later, the paired-associate verbal memory was labilized by exposing the subjects to one, two or four reminders. The List-memory was evaluated on Day 3 showing that the memory was improved when at least a second reminder was presented in the time window of the first labilization-reconsolidation process prompted by the earlier reminder. However, the improvement effect was revealed on Day 3, only when at least two reminders were presented on Day2 and not as a consequence of only retrieval. Therefore, we propose central concepts for the reconsolidation process, emphasizing its biological role and the parametrical constrains for this function to be operative.