If you are talking about California, '40 CA plates were yellow with black letters, the corners are very round in lieu of square like the '31-39 and '56, later.
The only way you can have a black/yellow plate on a car in CA is if the car was registered in CA prior to '73 with a black plate, that being when the blue/yellow plate came out. The registration would have to have been kept current or been on a non-op.
A black plate can be registered to a car in CA as a Year of Manufacture (YOM) however, the year of the vehicle has to be consistent with the years that the black plates were in use, 1963-73 and the validation stickers have to be the same year as the car the plate is being used on.. e.g. '66 Chevy, black plate with '66 stickers.
If you purchase a vehicle in CA that has black plates, the DMV will try to take them away from you, the clerks are instructed to do so. You might have to dig your heals in and resist the clerk, asking for a supervisor. If the registration fees have expired you are out of luck... A friend of mine just went through this on a '56 Ford.
I had a problem with my '36 Ford a couple of years ago, I have owned the car over 56 years... I had the car on a non-op and decided to renew the registration. Through a mistake the non-op had lapsed. The DMV wanted to take my black CA plates which have been on the car since 1963. The car has a '56 CA title.. I resisted... very strongly... To make a long story short, I took the CA validated registration cards from 1956 to 1998 and the non-op certificates into the DMV along with the Idaho Bill of Sale dated 1952, to prove I had owned the car since 1952.. I got to keep my black plates.