In this paper, analysis and trans-synthesis of acoustic bowed string instrument recordings with new non-negative matrix factorization (NMF) procedure are presented. This work shows that it may require more than one template to represent a note according to time-varying behavior of timbre, especially played by bowed string instruments. The proposed method improves original NMF without the knowledge of tone models and the number of required templates in advance. Resultant NMF information is then converted into the synthesis parameters of the sinusoidal synthesis. Bach cello suites recorded by Fournier and Starker are used in the experiments. Analysis and trans-synthesis examples of the recordings are also provided.