Twitter has emerged as a new application paradigm of sensing the physical environment by using human as sensors. These human sensed observations are often viewed as binary claims (either true or false). A fundamental challenge on Twitter is how to ascertain the credibility of claims and the reliability of sources without the prior knowledge on either of them beforehand. This challenge is referred to as truth discovery. An important limitation exists in the current Twitter-based truth discovery solutions: they did not explore the theme relevance aspect of claims and the correct claims identified by their solutions can be completely irrelevant to the theme of interests. In this paper, we present a new analytical model that explicitly considers the theme relevance feature of claims in the solutions of truth discovery problem on Twitter. The new model solves a bi-dimensional estimation problem to jointly estimate the correctness and theme relevance of claims as well as the reliability and theme awareness of sources. The new model is compared with the discovery solutions in current literature using three real world datasets collected from Twitter during recent disastrous and emergent events: Paris attack, Oregon shooting, and Baltimore riots, all in 2015. The new model was shown to be effective in terms of finding both correct and relevant claims.