Despite a myriad of studies that have been reported in analysing media discourse, few works take into account media bias. In response to this empirical gap, the present critical discourse study (CDS) aims to expose how the biggest national and International news media, The Jakarta Post and The New York Times construct the media bias in depicting Palestine and Israel regarding the latest conflicts in 2019 and 2020. The transitivity system of Halliday's systemic functional linguistics (SFL) was adopted to examine the textual features or choice of words in the clauses of 4 news articles from each news media. The findings show that both mainstream media have similarities, as if more favors to Palestine as the victim of the conflicts rather than Israel as a war criminal nation. However, The Jakarta Post and The New York Times have different sensitivities in constructing media bias. This empirical evidence suggests that critical discourse analysis (CDA) has a pivotal role in comprehending language used in media discourses. The last but not least, combining CDA and another theoretical approach is suggested for future studies.