It would be a good idea to keep the copyright notice in the code. It shows that you are not "stealing" the code from the original author and claiming it as your's [unintentionally].
*While open-sourced code can be copyrighted, if you made substantial changes to the code, you may have the right to remove the original copyright [upon notification of the original author. Does not apply if you have rewritten 99% of the code

].