He should be checked for a urinary tract infection.
Gail

I know another poster said check for urinary tract infection which is the
best idea to do before behavioral can be determined.

but  when they are outside  is it an enclosed yard where another cat can't
get in.  I going to bet it is not  what you are describing might be
territorial.  My spirit was spraying in doors I had all the test run and he
was clean.  Come to find out  he was spraying where the newspaper had been
left.  The newspaper is left by my mailbox  and some feral tom had been
marking the area.  I went and bought some deer urine and placed it around
the mail box and other marked spots no more feral tom coming around.

Also  could another cat be getting into your house thru the cat flap.  You
cat also might be responding to the other cats scent.

Most males that are not neutered @ the right age (ie: not neutered
before reaching sexual maturity), then in the vast majority of
incidents, they spray to cover the smell of a prior tom cat who has
been in his area. As cat's sense of smell is so superior to our own,
we can't smell what they can. All he is trying to do is set out his
territory. I know that this doesn't really help out, but it does go
someway to explaining why he does it.

You have two choices. One, follow Matthew's advise. Or two, get some
tom cat urine removal fluid. there are several on the market that
would suffice. I am providing a link to one product, but there are
many on the market to choose from. I suggest a quick search on the net
& I'm certain that you will find one that is suitable for you.

http://www.urine-off.co.uk/

You also need a back light to be able to spot the areas that are
affected, ( if you can't see of smell them already?)  As soon as the
smell goes, the chances are, so will the reason for your cat's desire
to remark it for you.
I hope this works for you.

Silknsox