For the first stage of the multi-sensitive bucketization (MSB) method, the l-diversity grouping for multiple sensitive attributes is incomplete, causing more information loss. To solve this problem, we give the definitions of the l-diversity avoidance set for multiple sensitive attributes and the avoiding of a multiple dimensional bucket, and propose a complete l-diversity grouping (CLDG) algorithm for multiple sensitive attributes. Then, we improve the first stages of the MSB algorithms by applying the CLDG algorithm to them. The experimental results show that the grouping ratio of the improved first stages of the MSB algorithms is significantly higher than that of the original first stages of the MSB algorithms, decreasing the information loss of the published microdata.