Gaussian mixture (GMM)-HMMs, though being the predominant modeling technique for speech recognition, are often criticized as being inaccurate to model heterogeneous data sources. In this work, we propose the stranded Gaussian mixture (SGMM)-HMM, an extension of the GMM-HMM, to explicitly model the dependence among the mixture components, i.e., each mixture component is assumed to depend on the previous mixture component in addition to the state that generates it. In the evaluation over the Aurora 2 database, the proposed 20-mixture SGMM system obtains WER of 8.07%, 10% relative improvement over the baseline GMM system. The experiments demonstrate the discriminating power that would be possessed by the mixture weights in their advanced form.