The reliable functioning of safety-critical IT systems depends heavily on the correct execution of programs. Deductive program verification can be performed to guarantee the correct execution to a large extent. There are already a plethora of programming languages in use, and new languages oriented toward high-reliability scenarios are still being invented. As a result, it is difficult to devise a full-fledged logical system for each language to support the verification of programs and prove the soundness and completeness of the logical system with respect to the formal semantics of the language. Language-independent verification techniques offer sound verification procedures parameterized over the formal semantics of programming languages. The specialization of the verification procedure with the formal semantics of a concrete programming language directly gives rise to a verification procedure for the language. This study proposes a language-independent verification technique based on big-step operational semantics. The technique features a unified procedure for sound reasoning about program structures that potentially cause unbounded behavior, such as iteration and recursion. In particular, the study employs a functional formalization of big-step operational semantics to support the explicit representation of the computation performed by the sub-structures of a program. This representation enables the exploitation of the auxiliary information provided for these sub-structures in the unified reasoning process. In addition, the study has proved the soundness and relative completeness of the proposed technique, evaluated the technique by verification examples in imperative and functional programming languages, and formalized all theoretical results and verification examples in the Coq proof assistant, and thus provides a basis for developing a language-independent program verifier with big-step operational semantics based on a proof assistant.