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A test oracle serves as a criterion or mechanism to assess the correspondence between software output and the anticipated behavior for a given input set. In automated testing, black-box techniques, known for their non-intrusive nature in test oracle construction, are widely used, including notable methodologies like differential testing and metamorphic testing. Inspired by the mathematical concept of inverse function, we present Retromorphic Testing, a novel black-box testing methodology. It leverages an auxiliary program in conjunction with the program under test, which establishes a dual-program structure consisting of a forward program and a backward program. The input data is first processed by the forward program and then its program output is reversed to its original input format using the backward program. In particular, the auxiliary program can operate as either the forward or backward program, leading to different testing modes. The process concludes by examining the relationship between the initial input and the transformed output within the input domain. For example, to test the implementation of the sine function $\sin(x)$, we can employ its inverse function, $\arcsin(x)$, and validate the equation $x = \sin(\arcsin(x)+2k\pi), \forall k \in \mathbb{Z}$. In addition to the high-level concept of Retromorphic Testing, this paper presents its three testing modes with illustrative use cases across diverse programs, including algorithms, traditional software, and AI applications.