NEW YORK (CNN/Money) - The number of job cuts planned by U.S. employers rose for the second straight month in May as firms announced plans to cut more than 73,000 jobs, an outplacement firm said Tuesday.

U.S. businesses announced 73,368 job cuts in May, up from 72,184 job cuts in April, a gain of 1.6 percent, according to Chicago-based Challenger, Gray & Christmas, which keeps track of monthly job-cut announcements.

May's announcements were 6.9 percent higher than those of May 2003, when 68,623 cuts were announced.

Through the first five months of 2004, employers have announced 408,392 job cuts, an average of 81,678 per month, or about 28 percent lower than the 114,163 pace in the first five months of 2003.

But the 12-month moving average of announcements rose to 89,500 from 89,105 in April, the first gain in the moving average since December.

And the number of job-cut announcements per month remains well above pre-recession levels of about 51,000 per month, CEO John Challenger said in a release.

"Overall, job cuts are down from last year and significantly lower than the record numbers we saw in 2002 and 2001, but there are still some worrisome trends," Challenger said.

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Challenger cited recent heavy job-cutting announcements in retail -- 10,868 announcements in May -- and financial services -- 6,113 announcements in May -- and industrial goods -- 6,734 cuts in May -- as worrisome signs for the health of the labor market.

Still, the job market is much improved from a year ago. Non-farm payrolls have grown by more than 250,000 jobs in each of the past two months and have added more than 700,000 jobs this year, according to the latest data from the Bureau of Labor Statistics.

On Friday, the BLS is scheduled to report on May unemployment and non-farm payroll growth. Economists, on average, expect the jobless rate to hold steady at 5.6 percent and for about 215,000 new jobs to be created.

In May, Challenger, Gray & Christmas also kept track of hiring plans for the first time and found that 55,307 new jobs were announced. Like the job-cut data, this number is not seasonally adjusted, and offers no information about when those jobs will actually be created.

Florida led the nation in job-cut announcements in May, with 12,874. Virginia followed with 11,277 announcements, Pennsylvania had 8,020, Illinois had 6,445 and Michigan had 4,683.