Privacy preserving data publishing (PPDP) refers to the releasing of anonymized data for the purpose of research and analysis. A considerable amount of research work exists for the publication of data, having a single sensitive attribute. The practical scenarios in PPDP with multiple sensitive attributes (MSAs) have not yet attracted much attention of researchers. Although a recently proposed technique (p, k)-Angelization provided a novel solution, in this regard, where one-to-one correspondence between the buckets in the generalized table (GT) and the sensitive table (ST) has been used. However, we have investigated a possibility of privacy leakage through MSA correlation among linkable sensitive buckets and named it as “fingerprint correlation fcorr attack.” Mitigating that in this paper, we propose an improved solution “c,k-anonymization” algorithm. The proposed solution thwarts the fcorr attack using some privacy measures and improves the one-to-one correspondence to one-to-many correspondence between the buckets in GT and ST which further reduces the privacy risk with increased utility in GT. We have formally modelled and analysed the attack and the proposed solution. Experiments on the real-world datasets prove the outperformance of the proposed solution as compared to its counterpart.