We study the anonymization technique of k-anonymity family for preserving privacy in the publication of microdata. Although existing approaches based on generalization can provide good enough protections, the generalized table always suffers from considerable information loss, mainly because the distributions of QI (Quasi-Identifier) values are barely preserved and the results of query statements are groups rather than specific tuples. To this end, we propose a novel technique, called the Mutual Cover (MuCo), to prevent the adversary from matching the combination of QI values in published microdata. The rationale is to replace some original QI values with random values according to random output tables, making similar tuples to cover for each other with the minimum cost. As a result, MuCo can prevent both identity disclosure and attribute disclosure while retaining the information utility more effectively than generalization. The effectiveness of MuCo is verified with extensive experiments.