Its fairly typical of a Basenji not to want to soil his own domain. I've had many over the years and owners of our puppies have experienced the same thing. NOT at home ! We have about 2/3 of an acre of garden including lawns, borders, shrubbery, orchard - plenty of space, you'd think, for a Basenji to do his/her business. But some never have and never would.
One other Basenji mine walk with (run free with) in the woods goes one better, he won't even pee in his own garden but saves it up for the woods. When he pees, it lasts often for over a minute and can't be good for him. Having pee-d - he then finds a hiding spot and defecates.
In the woods (or out on a more conventional walk) - NEVER at home !
Sorry, but like other things, I don't give the dogs a lot of choices about where to potty. I'd try the poop in the yard. Failing that, I'd matchstick then praise like crazy, then take a walk. There are times we cannot walk them and having had ruptured anal glands with Cara, regular pooping isn't an option. Road trips, they learn "go poop".
Debra
@debradownsouth You probably need to explain the "matchstick" technique.
@senjisilly It's not always possible to walk the pup after walk particularly in the winter so I'd love to have my pup use the fully fenced backyard. She too seems to prefer to "hold". Could someone fully explain the "matchstick" practice and how it works? Thanks in advance.
Sorry, was out all day. The matchstick doesn't need to be the sulfur side in. In fact, I DON'T use that side. I also use vaseline, not spit. Vets use this also or tell clients to do so with dogs after a surgery that don't want to potty due to discomfort. It's safe, and I have only had one dog ever who it didn't work for. So I had to add fiber and stool softener so her need to potty outweighed her need to not get her feet wet.
As for the article's drama on surprised dogs, dogs don't really take it personally or with embarrassment. They just want it out.
The only matches I would ever use are no longer obtainable. Spanish book matches. They are (were) just wax paper tightly rolled into a stick. They did the job but its been years since I've seen one and friends with a house in Spain have never met them.
Sally in desperation once, I used a birthday candle. It works. 
Debra
@debradownsouth said in My basenjis have a new yard, but won't poop there. Any recommendations?:
Sally in desperation once, I used a birthday candle. It works
It would ! I hadn't thought of that (am too old now to have candles on a birthday cake anyway) but that would be a good stand-by at need.
Hi, we have 2 basenji boys. Eldest never poos in garden. Except emergencies..... Our 2nd did poo for a year or two at first. But suddenly realised his brother doesn't. So.... Now he won't.. So walks it is. They go on morning walk. 7am ish. And ask#, around 4.30 for another. I can set my watch by second poop... 
@erica-ruth said in My basenjis have a new yard, but won't poop there. Any recommendations?:
I can set my watch by second poop
My first ever Basenji, Donner, back in the very early 1980s learned from very young that as soon as he'd emptied, we'd turn and head back home. Lady, who arrived in the household just four days after Donner and long before we totally dog-proofed the garden, so walks were necessary, did her business as and when she needed to. But Himself no - to prolong the walk he'd hang on for (sometimes) miles !
When the first litter came along, we did totally fence the entire garden so as to keep the pack safe. It was only later, after several litters developed a penchant for fresh vegetables straight off the plant, Brussel Sprouts, sweet corn, cucumbers, raspberries etc, that we had to fence off the vegetable garden to protect it from the marauding hordes. The herb garden had to be isolated too, or we'd have even sweeter smelling puppies than normal.
