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Properties of negative initial leaders (NILs) and flash size in a cluster of supercells with generally inverted charge structure in Oklahoma on 10-11 May 2010 are examined, primarily using Lightning Mapping Array data. A method to identify NILs from Lightning Mapping Array source is proposed and helps to reveal the multiple NILs properties and their distributions. The NILs in the supercell cluster have smaller speed (median 3-D displacement speed: 0.65 x 105 m/s), relative to the previous reports in normal thunderstorms. Furthermore, median NIL speeds initially decrease with increasing height but begin increasing above 12 km. The NILs tend to decelerate during the early stage. The parameters characterizing flash duration and spatial size are also investigated. It is found that they all follow lognormal distributions and the spatial flash size is relatively small on average (median horizontal distance: 5.54 km). Most flashes (83.18%) extend primarily in the horizontal direction. Flash area shows an inverse relationship with flash density at their fast changes during storm evolution. Although large flash initiation density (FID) generally occurs in regions with small flash size, the smallest flash size is nearly not collocated with large FID value. In the regions with large FID, average flash duration roughly increases with increasing FID, while average flash area changes little. We proposed that the pattern of charge pockets and variation of charge density dominated by the strong kinematics are responsible for some new findings about the properties of NIL and flash size in the supercell cluster.