Our aim is to prove the following result. Let the 2-torsion-free rings be \( \mathfrak {U} \) and \( \mathfrak {V} \) , such that both are semiprime or fulfill the conditions of Fact A, and let \( \mathfrak {R} \) be a 2-torsion-free faithful \((\mathfrak {U}, \mathfrak {V})\) bimodule possessing the property in case \( r \in \mathfrak {R} \) and \( \mathfrak {U}r = \{0\} \) (resp. \( r\mathfrak {V} = \{0\} \) ), then \( r = 0 \) . If \( \mathfrak {J} \) is a Jordan biderivation that commutes on the triangular ring \( \mathfrak {P} = {Tri}(\mathfrak {U}, \mathfrak {R}, \mathfrak {V}) \) , then \( \mathfrak {J} \) is zero. Moreover, we establish that every Jordan biderivation that commutes on a triangular ring under a specific setting is precisely a zero map.
