Milo Janus is a health guru and the owner of many franchises. One of his partners, Gene Stafford, has begun to suspect Janus' many crooked schemes and is starting an audit. Janus denies everything but begins to plot Stafford's murder. That night, he sets up a part at 9 but at 7 goes to the gym where Stafford is alone. He tries to strangle Stafford with a pipe but Stafford spills coffee on Janus' arm, runs across a gym (in his street shoes), and gets grabbed by Janus who finishes what he started. Janus then dresses the corpse in his exercise clothing (including sneakers), puts him on a weight-lifting bench, and makes it look like Stafford dropped the barbell and died.
Janus then takes a bit of tape from the recorder that records his call, with a bit of Stafford's voice on it. At the party two hours later, he goes into the other room after unplugging the second phone-line light he is calling from, rings the phone, and plays the tape for his secretary, also present. She calls Janus to the phone and he stages a fake conversation where he talks about how Stafford is changing into his gym clothing and going to exercise. Janus even "warns" him not to do it. His alibi set, Janus goes on to enjoy the party.
The next day Columbo arrives at the gym during the investigation. He notices the scuff marks on the gym floor and quickly determines that it was waxed the previous night before 7. The scuff marks are brown - none of the police present have brown shoes, but Stafford's shoes in his locker do. The marks are those of someone who was running and turning. Columbo also notices the clean coffee cup and pot but the spilled coffee stain and the garbage can filled with Chinese food containers.
Columbo goes to visit Janus, who with his secretary's unwitting help affirms his alibi. Columbo is more interested in the burn on Janus' arm, which looks like it might have been caused by...hot coffee. Columbo notes that if Stafford were planning on exercising he wouldn't have eaten a heavy Chinese meal, but Janus dismisses it, noting Stafford wasn't very smart about exercising.
Columbo talks to the divorced man's widow and soon realizes the guy suspected Janus of something. Columbo begins to put the pieces together as he notices the light out on Janus' phone. He also finds out that Janus tapes all of his calls, and that the secretary has never been at Janus' home but "Gene" didn't express any surprise or reaction when she answered the phone at the party. While trying to track down an accountant who was investigating Janus on Stafford's behalf, Columbo gets his answering machine and realizes that it's easy to assume a pre-recorded voice is real.
Mrs. Stafford gets the news about some of what Janus was up to from the accountant and confronts Janus, who denies everything. Furious and depressed, she throws a drink in his face and leaves, but later, depressed, tries to kill herself. Columbo angrily confronts Janus at the hospital and warns him that Mrs. Stafford's attempted suicide is on his head as well. Janus angrily denies everything and asserts Columbo has no proof even if Janus can't account for his whereabous at 7 p.m. - the call proves Stafford died at 9. As Columbo leaves, he notices a mother tying her son's shoesv and puts it all together.
Later at his offices, Janus gets a call from Gene Stafford. He storms out into the office to find...Columbo, playing a bit of the recorded tape. Columbo has a search warrant, and confronts Janus with the truth: he knows how Janus did it. How he used the tape to rig his alibi, strangled Stafford, made it look like an accident, got back to the house, took the call. But Columbo now has evidence that someone else dressed Stafford: his exercise shoes were tied in reverse for a right-handed man and compared to his normal street shoes in the locker. Someone else dressed Stafford, and was present when Stafford was killed.
Janus asserts it could have been anyone - nothing proves it was him. But Columbo has him - at the party in front of witnesses, and in his sworn disposition, Janus swore that during the phone call Gene said he was changing his clothes, the exercise clothes he was found in the next day. Since Gene didn't change his own clothes, only one person could have known he was changing his clothes - the murderer. As Columbo notes, "You tried to contrive the perfect alibi, sir. And it's your perfect alibi that's gonna hang you."