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Subunit segmenting and modelling in medical sign language is one of the important studies in linguistic-oriented and vision-based Sign Language Recognition (SLR). Many efforts were made in the precedent to focus the functional subunits from the view of linguistic syllables but the problem is implementing such subunit extraction using syllables is not feasible in real-world computer vision techniques. And also, the present recognition systems are designed in such a way that it can detect the signer dependent actions under restricted and laboratory conditions. This research paper aims at solving these two important issues (1) Subunit extraction and (2) Signer independent action on visual sign language recognition. Subunit extraction involved in the sequential and parallel breakdown of sign gestures without any prior knowledge on syllables and number of subunits. A novel Bayesian Parallel Hidden Markov Model (BPaHMM) is introduced for subunit extraction to combine the features of manual and non-manual parameters to yield better results in classification and recognition of signs. Signer independent action aims in using a single web camera for different signer behaviour patterns and for cross-signer validation. Experimental results have proved that the proposed signer independent subunit level modelling for sign language classification and recognition has shown improvement and variations when compared with other existing works.