Our team maintains a noncompetitive working relationship where everyone supports each other.

noncompetitive 是由前缀 non-（表示"非、不"）和形容词 competitive（竞争的）组成的复合词。competitive 来自动词 compete（竞争），加上形容词后缀 -ive 构成。noncompetitive 整体意思是"非竞争性的"，指不涉及竞争或对抗的状态。