How do you train two cats to get along?

[ton ton]

My cat fights with the cat next door. She's female and he's male both spayed/neutered.
We were in the garden yesterday and next door's cat turned up. They sat on the lawn one on either side of us for a bit, but one was always staring at the other, and when our cat got up, next door's cat went over to her and a fight nearly ensued before we got in between them.
When they're outside they often fight and our cat comes back with scratches, but next door's cat is enormous and could hurt her much worse if he wanted.
Should we be breaking them up or letting them fight or what?

[door]

A chair and a whip?

[pradeepa]

let them fight

[stevesherri]

why let them run loose?
pets should be contained to their own yard/home.

[Eddie R]

I'm afraid it seems as if your garden may be part of your neighbour's cat's territory. If you don't want your cat attacked you may need to keep it in. It is ossible that if your cat is attacked and ecomes submissive to the neighbour's cat it may not attack any more, but sjhe could get badly hurt in the process, so its probably better to keep her in.