The phrase "a firm eye" is correct and usable in written English.
It can be used to describe someone who is observant, attentive, or has a strong focus on something.
Example: "The manager kept a firm eye on the team's progress to ensure they met their deadlines."
Alternatives: "a watchful eye" or "a keen eye".
She is enormously patient, gentle, loving and yet keeps a firm eye on what is going on.
The glass bowl lifts from the base so you can keep a firm eye on your creations – from cakes to perfect dough.
Nonetheless, leaders on both sides must make the Trans-Atlantic Trade and Investment Partnership a reality, keeping a firm eye on the final goal.
And true to what locals would call the spirit of Chennai, it means a nod to the future while keeping a firm eye on the past.
Don't worry – he kept a firm eye on it and guinea was safely returned to school on Monday in its sad little wooden cage.
The paper concludes that improving the financial architecture in a disciplined, consistent, internationally coordinated and sustained manner with a firm eye to the public interest should ultimately be centered on market discipline.
Thanks partly to its narrower focus, Daniel Snowman's keeps a firmer eye on the main issue.
Juvena carries a firming eye cream ($36 at Sephora), and Zirh offers an after-sun cooling gel ($22.50 at Bloomingdale's).
National parties, which control party lists for Euro-elections, not to mention jobs for defeated or homesick Euro-MPs, also keep a firmer eye these days on Euro-MPs' loyalty.
"We don't want to kill an already weak economy, but we want to make sure everyone understands we have a very firm eye on inflation".
Weale's submission was published 24 hours after the incoming deputy governor of the Bank, Sir Jon Cunliffe, said Threadneedle Street would keep a "very firm eye" on lenders as Help to Buy was rolled out.
