Celia Lipinski of Racine, Wis., wanted to donate her kidney to her 49-year-old sister Paula, who had acute kidney failure (search) and had been on dialysis for nearly two years.

But despite Lipinski's courage and generosity, her kidney was not a match for Paula.

Hundreds of miles away in Twinbridge, Ohio, 36-year-old Claudia Lillibridge and her husband, Doug, 33, were experiencing the same frustration. Claudia wanted to donate a kidney to Doug, who suffered from diabetes since he was 10 years old and for the past several years had been suffering kidney failure and undergoing renal dialysis three times a week.

But a computerized program that arranges kidney swaps for pairs of patient-donors who do not match each other but fit with another pair, allowed a solution and the Lipinski and Lillibridge families were able to participate in a four-way kidney exchange. Doug Lillibridge received the kidney Celia Lipinski had tried to donate to her sister, and Paula Lipinski received the kidney Claudia Lillibridge had wanted to give her husband.

Click in the video to watch Bridget Quinn's full interview with Doug and Claudia Lillibridge.

The Lipinskis and Lillibridges found each other through Ohio's Paired Donation Kidney Consortium (search), the first state-sponsored program to arrange such matches. It's one of only three live-paired donation programs in the nation.

The procedure, performed June 7 at University Hospitals of Cleveland, was the fourth pair of transplants performed since the consortium was formed by the Ohio Health Department in 2003.

One week after the operation, all four patients were doing well.

Doug Lillibridge, who had been waiting for a donor match for eight months and had considered a riskier procedure that would have made his body more receptive to Claudia's kidney, said the swapping program offers hope for all kidney patients.

"With this new program, hopefully it will increase the chance of someone finding [a match] sooner," he said.

For Claudia Lillibridge, the personal connection with the Lipinskis brought a positive note to a frightening situation.

"It was tremendous, it made it real," Claudia Lillibridge told FOX News. "When we had the opportunity to sit down and meet these beautiful, lovely people, my gratitude was — no words can describe the feelings I felt," she said. "We were lifesavers to them, and they were lifesavers to us."

The Ohio program is operated by nine Ohio hospitals. Eight hospitals in Michigan and at least one in Indiana are expected to join the Ohio consortium this month.

"This will give us the largest single potential donor database in the nation," said Dr. Mark Aeder, a UHC surgeon and committee member of the consortium. "The program is designed to increase the number of organs available for transplantation, decrease waiting times for patients and increase transplant success rates by identifying more live donors."

Johns Hopkins University (search) in Baltimore runs a similar paired donor program, as do six New England states.

Kidney transplant specialists are pushing for a nationwide program.

"It really is a way to save lives," said Cathy Paykin, transplant program director at the National Kidney Foundation (search). "So often, a person has a potential donor who's emotionally connected to them, but they just don't match."

There are more than 60,000 U.S. patients awaiting kidney transplants. Last year, 3,718 on the waiting list died because suitable organs couldn't be found in time, according to the National Kidney Foundation.

Between 2001-2004, 55 paired transplants were performed and the practice is increasing, according to the United Network for Organ Sharing (search).

Dr. Aeder said paired donations don't just help those who are involved. They also take two names off the waiting list for kidneys where the average wait is three to four years.

Joining Dr. Aeder in the four surgeries were Drs. James Schulak, Christopher Siegel and Juan Sanabria. The four physicians also are faculty members in the Department of Surgery at the Case Western Reserve University School of Medicine.

As for the Lipinskis and Lillibridges, the cross kidney transplant won't be the end of their connection. E-mails, addresses and phone numbers have been exchanged, and Claudia said the pairs have discussed working together to raise awareness for the program.

"We're part of each other now," Paula Lipinski said.

FOX News' Robin Wallace, Amy Sokoloff and Bridget Quinn, and The Associated Press contributed to this report.