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In this paper, we propose a novel representation of the FMLLR transform. This is different from the standard FMLLR in that the linear transform (LT) is expressed in a factorized form such that each of the factors involves only one parameter. The representation is mainly motivated by QR-decomposition of a square matrix and hence is referred to as QR-FMLLR. The mathematical expressions and steps for maximum likelihood (ML) estimation of the parameters are presented. The ML estimation of QR-FMLLR does not require the use of numerical technique, such as gradient ascent, and it does not involve matrix inversion and computation of matrix determinant. On an LVCSR task, we show the performance of QR-FMLLR to be comparable to the standard FMLLR. We conjecture that QR-FMLLR is amenable to speaker adaptation using data that varies from very short to large and present a brief discussion on how this can be achieved.