The phrase "looked square eye" is often used to describe a focused and intense gaze. There are several synonyms that can be used to convey a similar meaning, such as "stared," "gazed," "fixed one's eyes on," "peered," and "glared." Each of these words implies a concentrated and deliberate act of looking, emphasizing a cautious or scrutinizing approach. Other related terms might include "inspected," "scrutinized," "surveyed," or "examined," each of which implies a more deliberate and analytical approach to looking at something. Whatever synonym you choose, it should convey a sense of intense concentration and focus, applying all of one's attention to a specific object or situation.