Rank-constrained spatial covariance matrix estimation (RCSCME) is a state-of-the-art blind speech extraction method applied to cases where one directional target speech and diffuse noise are mixed. In this paper, we proposed a new algorithmic extension of RCSCME. RCSCME complements a deficient one rank of the diffuse noise spatial covariance matrix, which cannot be estimated via preprocessing such as independent low-rank matrix analysis, and estimates the source model parameters simultaneously. In the conventional RCSCME, a direction of the deficient basis is fixed in advance and only the scale is estimated; however, the candidate of this deficient basis is not unique in general. In the proposed RCSCME model, the deficient basis itself can be accurately estimated as a vector variable by solving a vector optimization problem. Also, we derive new update rules based on the EM algorithm. We confirm that the proposed method outperforms conventional methods under several noise conditions.