The Dow Jones Industrials jumped a moderate amount on Monday, up more than 46 points to close at 51,078.88.
The new climb reflects a record high closing, with the S&P 500 and the Nasdaq also reaching records too.
The Dow reflected modest gains of about one point, with consumer retailers and technology stocks conducting a tug-of-war campaign for investors' money.
The price of oil, which usually moves markets, was up on Monday, rising about 5-percent on the day, based on concerns about whether there will be an agreement with Iran for a peace deal that could reopen the Strait of Hormuz, the closing of which has choked off about one-fifth of oil and related products.