Yes, self-plagiarism is certainly possible and it's just as serious.

Self-plagiarism, or "double-dipping," is deception and goes against the core principles of ethical writing. Papers are assigned for you to demonstrate what you have learned in a particular class. If you reuse a paper you wrote for a previous class, you are not demonstrating new learning.

• Turning in a paper for a current class that you already submitted as an assignment for a previous class
• Using a substantial amount of a paper written for another course as content for a new assignment
• Treating anything you've previously written as if it were new material

How to avoid self-plagiarism:

• Don't reuse old papers!
• Cite yourself: cite your previous work just as you would cite other people's research, quotation marks and all.
• Get permission! If you strongly feel the need to reuse material you've written for another class, get permission from BOTH professors, the current one and the one for whom you wrote the original paper.