Separating the singing voice from a musical mixture is a problem widely addressed due to its various applications. However, most approaches do not tackle the separation of unvoiced consonant sounds, which causes a loss of quality in any vocal source separation algorithm, and is especially noticeable for unvoiced fricatives (e.g. /T/ in thing) due to their energy level and duration. Fricatives are consonants produced by forcing air through a narrow channel made by placing two articulators close together. We propose a method to model and separate unvoiced fricative consonants based on a semisupervised Non-negative Matrix Factorization, in which a set of spectral basis components are learnt from a training excerpt. We implemented this method as an extension of an existing well-known factorization approach for singing voice (SIMM). An objective evaluation shows a small improvement in the separation results. Informal listening tests show a significant increase of intelligibility in the isolated vocals.