This paper addresses the challenge of estimating the relative transfer function (RTF) vectors of multiple speakers in a noisy and reverberant environment. More specifically, we consider a scenario where two speakers activate successively. In this scenario, the RTF vector of the first speaker can be estimated in a straightforward way and the main challenge lies in estimating the RTF vector of the second speaker during segments where both speakers are simultaneously active. To estimate the RTF vector of the second speaker the so-called blind oblique projection (BOP) method determines the oblique projection operator that optimally blocks the second speaker. Instead of blocking the second speaker, in this paper we propose a covariance blocking and whitening (CBW) method, which first blocks the first speaker and applies whitening using the estimated noise covariance matrix and then estimates the RTF vector of the second speaker based on a singular value decomposition. When using the estimated RTF vectors of both speakers in a linearly constrained minimum variance beamformer, simulation results using real-world recordings for multiple speaker positions demonstrate that the proposed CBW method outperforms the conventional BOP and covariance whitening methods in terms of signal-to-interferer-and-noise ratio improvement.