Linux: how to remove ^M at each line end

I got an acsii file from a Window's user. If it is a regular windows text file, then I can use a command 'dos2unix' to convert it in unix format. However, it doesn't work. I use 'less' to have a look at it, it looks like:

line1^M line2^M

. If I use emacs to view it, it looks okay like a regular file. In order to convert it to unix format, I use 'gedit' to do the conversion. A user will be reminded that you save as which format...