The free induction decay (FID) transversal data determines the measurement accuracy of time-dependent geomagnetic fields, whereas the conservation of clean components and removal of noise cannot be easily achieved for this kind of data. Even though numerous techniques have been proven to be effective in improving the signal-to-noise ratio by filtering out frequency bands, how to efficiently reduce noise is still a crucial issue due to several restrictions, e.g., prior information requirement, stationary data assumption. To end this, a new multivariate algorithm based on the fusion of principal component analysis (PCA) and singular value decomposition (SVD), namely, principal component analysis and decomposition (PCAD), was presented. This novel algorithm aims to reduce noise as well as cancel the interference of FID transversal data. Specifically, the PCAD algorithm is able to obtain the dominant principal components of the FID and that of the noise floor by PCA, in which an optimal number of subspaces could be retained via a cumulative percent of variance criterion. Furthermore, the PCA was combined with an SVD filter whose singular values corresponding to the interferences were identified, and then the noise was suppressed by nulling the corresponding singular values, which was able to achieve an optimum trade-off between the preservation of pure FID data and the denoising efficiency. Our proposed PCAD algorithm was compared with the widely used filter methods via extensive experiments on synthetic and real FID transversal data under different noise levels. The results demonstrated that this method can preserve the FID transversal data better and shows a significant improvement in noise suppression.