Gene expression data matrices often contain missing expression values. In this paper, we describe a new algorithm, named improved fixed rank approximation algorithm (IFRAA), for missing values estimations of the large gene expression data matrices. We compare the present algorithm with the two existing and widely used methods for reconstructing missing entries for DNA microarray gene expression data: the Bayesian principal component analysis (BPCA) and the local least squares imputation method (LLS). The three algorithms were applied to four microarray data sets and two synthetic low-rank data matrices. Certain percentages of the elements of these data sets were randomly deleted, and the three algorithms were used to recover them. In conclusion IFRAA appears to be the most reliable and accurate approach for recovering missing DNA microarray gene expression data, or any other noisy data matrices that are effectively low rank.