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Cross-language programming is a common practice within the software development industry, offering developers a multitude of advantages such as expressiveness, interoperability, and cross-platform compatibility, for developing large-scale applications. As an important example, JNI (Java Native Interface) programming is widely used in diverse scenarios where Java interacts with code written in other programming languages, such as C or C++. Conventional static analysis based on a single programming language faces challenges when it comes to tracing the flow of values across multiple modules that are coded in different programming languages. In this paper, we introduce CSS, a new Caller-Sensitive Specification approach designed to enhance the static taint analysis of Java programs employing JNI to interface with C/C++ code. In contrast to conservative specifications, this approach takes into consideration the calling context of the invoked C/C++ functions (or cross-language context), resulting in more precise and concise specifications for the side effects of native code. Furthermore, CSS specifically enhances the capabilities of Java analyzers, enabling them to perform precise static taint analysis across language boundaries into native code. The experimental results show that CSS can accurately summarize value-flow information and enhance the ability of Java monolingual static analyzers for cross-language taint flow tracking.