If you describe someone's eyes or expression as unblinking, you mean that they are looking steadily at something without blinking. He stared into Leo's unblinking eyes. + unblinkingly un·blink·ing·ly She looked at him unblinkingly. unblinking stare/gaze
{s} not blinking; not shutting and opening the eyes; not showing a response; unafraid, unfaltering, unflinching
not shrinking from danger showing no visible emotion; "stood unblinking and accepted a sentence of a year