Multilingual LLM-as-a-judge is widely used to evaluate model outputs across languages, but suffers from cross-lingual inconsistency (Fu and Liu, 2025). Existing methods typically treat this inconsistency as noise and mitigate it through voting or aggregation. In this work, we instead show that multilingual inconsistency can provide complementary evaluation signals. Our oracle analysis finds that sampling judgments across languages yields a higher performance upper bound than single-language judging, indicating that different languages potentially include complementary judgments. Motivated by this finding, we propose SEMJ, a self-evolving multilingual judge that leverages cross-lingual inconsistency for iterative refinement. SEMJ constructs multilingual variants of each input, collects independent judgments and rationales, and feeds inconsistent outputs back for self-reflection and re-evaluation. Experiments on multiple benchmarks show that SEMJ consistently outperforms voting and reflection baselines in both accuracy and cross-lingual consistency. Further analysis shows that inconsistency triggers useful re-evaluation, which improves judgment quality.