Large language models (LLMs) take advantage of step-by-step reasoning instructions, e.g., chain-of-thought (CoT) prompting. Building on this, their ability to perform CoT-style reasoning robustly is of interest from a probing perspective. In this study, we inspect the step-by-step reasoning ability of LLMs with a focus on negation, which is a core linguistic phenomenon that is difficult to process. In particular, we introduce several controlled settings (e.g., reasoning in case of fictional entities) to evaluate the logical reasoning abilities of the models. We observed that dozens of modern LLMs were not robust against lexical negation (e.g., plausible→implausible) when performing CoT-style reasoning, and the results highlight unique limitations in each LLM family.