No, PowerDirector 16 cannot produce videos with transparent background.
As far as I know, PowerDirector 17 cannot produce transparency as well.
In the effects of Cyberlink, there are no videos with transparency, but PNG-picture files as sequences. PNG pictures can have transparency.

Hatti Win 10 64, i7-4790k, 32GB Ram, 256 GB SSD, SATA 2TB, SATA 4TB, NVidia GTX1080 8GB, LG 34" 4K Wide, AOC 24" 1080

So I created an animated video and rendered it as PNG files, MP4, and AVI. When I import into Power Director, the PNG files retain the transparent background, which I need so I can overlay the object on top of other objects. However, there are dozens of PNG files (one for each frame), so positioning each of them is unrealisitic. The AVI files and MP4 files, however, show a black background when they are imported into Power Director, so I cannot use them. It is making me insane. So how can get the AVI or MP4 files to retain their transparency when I import them, or, how can I move the PNG files as one unit, so I can position them on the screen? I have produced the transparent PNG files in both AVI and MP4 formats in PowerDirector as well, but the background always turns black when I do it. HELP!!!

Just discovered the COMBINE option, which lets me turn the transparent PNG files into one unit so I can position on screen, and the group/ungroup feature, but they do not seem to allow me to reposition the PNG files as one unit.

Quote ... I have produced the transparent PNG files in both AVI and MP4 formats in PowerDirector as well, but the background always turns black when I do it. HELP!!!

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Apply Chroma key for the black and the black becomes transparent.

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Apply Chroma key for the black and the black becomes transparent.

WOW, I had no idea about that. Thank you so much. I will give it a try (once I figure out how). Much appreciated.

Worked like a charm! Thanks!