Recording a Skype call could come in handy in other ways, too. For example, you could record a conference call so that you have a record of it later.
Of course, always keep in mind that you DO want to make sure the other party knows they’re being recorded. In many places, it is illegal to record somebody without their knowledge. Just keep that in mind. And, I’m not weird enough to be a lawyer, so keep that in mind, too. 
Recording Skype Calls On Windows
Under Windows, there are several solutions such as:
None of these are free, but they’re not expensive at all. And, of the 3, Pamela is the one I’ve heard the most about. It does have a freeware version, but it is limited to 15-minute recordings.
All profess to record both audio and video. So, you can not only get the audio recording, but you can do things like side-by-side video, etc.
Note