Rear suspension banging.

I wish I could point to just one issue and say "this is it" but when you are dealing with the rear suspension or rear end are too many potential candidates to look at. For example, have you had the rear shocks checked? It might be the bushing at the top or it might be that the nuts and bolts at the top and bottom need adjustment. Or it could be that the exhaust system is loose and banging against the body. It also might be a loose rear suspension member that is banging against its carrier. Or, it could be something as simple as flat-spotting on your Jazz's rear tires. So, what do I think it is? I am tempted to say it is likely related to a loose bushing on one of your Jazz's shocks. The bushing is a hard-rubber piece at the top of the shock. If it is loose, it could be banging against the cover and creating the sound you hear. If you feel competent to check this problem, you will need a good pneumatic jack to lift the rear end and keep it up safely. Never use the scissors jack that came with your Jazz because it is not designed to keep your vehicle in the air so you can work on it. Use it only when you are changing tires. This is a problem that should be addressed when you have time as it should not affect your car's handling. It is more of an annoyance than anything else. To see if there might be other issues affecting you Jazz, look at http://www.safecar.info.

Check your rear shocks. On the fender, push with your body going down. Upon releasing, your car should go up and down one time then settle. If it goes beyond or hesitate to move, you have a problem with your shocks. I think you also have a problem with the shock absorber bush. It does not matter if you have a new or old shock absorber. The lifespan of the shocks depends on the way you drive on bumpy roads.

It could be a number of items.

1. The rear suspension components.
The noise may be emanating from a failed shock absorber.
There could also be a number of failed rubber bushes in one or more rear suspension components that is allowing metal to metal contact.

2. If an exhaust hangar on the exhaust system has broken the exhaust system will swing and bang against the underside of the vehicle.

You need to get the car on a hoist with the rear wheels removed to inspect all items and identify the likely source of the noise.

it is a common problem for the top mountings on the rear dampers to fail worth checking them

You may have to remove the tires but they are very well known for braking the front coil springs.

check your sway bar link pins they probably are broken in the back .

There is no adjustment,it sounds like you need some new struts.

ON MINE IT WAS THE WISH BONE BUSHES, CHANGED ALL WITH THE POLYUATHANE DONE THE JOB

need an eyeball inspection when off the ground

broken exhaust mounts
shock /strut tower failure
*
these not normally cause a metal to metal banging noise
lower swing arm arm bushes
hub bearing
rear brake pads worn to metal

It could be your subframe as well big problem with E36's. Also you can check your Rear Shock Mounts in the trunk by removing the carpet, they are under the speakers. Also check your brake pads, the little shim could have fallen off causing your brake pad to rattle over bumps. And check all your heat shields.