Bill Belichick has made trades with all 31 teams around the NFL since resigning as head coach of the New York Jets in 2000. But the napkin note that read, “I resign as HC of the NYJ,” would kickstart the last deal between New York and Belichick’s imminent destination for 20 seasons.

Remember the first-round compensation that became defensive end Shaun Ellis?

That drought ended last week when the New England Patriots agreed to send veteran wide receiver Demaryius Thomas to the Jets in exchange for a sixth-round pick in the 2021 draft.

“I would say there was a certain period of time when there’s no way this transaction would’ve happened,” Belichick told reporters on his conference call Tuesday. “But during other periods of time, yeah. Again, we don’t want to help the Jets. They don’t want to help us. We’re in the same division. They’re not the easiest trades to make, but if the trade is good for both teams, ultimately what we’re trying to do is improve our team.”

The 2-0 Patriots will host the 0-2 Jets for a 1 p.m. ET kickoff this Sunday at Gillette Stadium. The AFC East counterparts will meet again in October at MetLife Stadium.

Time will tell how much Thomas, who caught one pass in his Jets debut Monday night before exiting with a hamstring injury, factors in.

“We have 14 other games to play besides the games against the Jets,” Belichick said. “Do we want to help them? Do they want to help us? No and no. But in the end, if it helps us in the other 14 games and helps our team, then it’s something that’s worth considering. Look, we’ll try to help our team in any way we can. Not saying that those trades within the division – you don’t have to analyze them a little bit more closely.”

The Patriots had acquired center Russell Bodine, who has since been released, from the Buffalo Bills leading up to the 53-man roster deadline. Quarterback Drew Bledsoe and slot receiver Wes Welker also stand among the divisional swaps from Belichick’s tenure.

“We’ve done it before certainly with Miami with a player like Welker or Buffalo with a player like Bledsoe,” added Belichick. “Those weren’t insignificant players at that time. In the end, I want to do what’s best to help our football team, and I don’t want to try to help our opponents that much. But you have to give up something to get something.”

Even if that something requires a double-take.

“When you look at the beginning of each year, inter-division trading is probably not something you would think is going to be at the top of the list,” Belichick said.