no, it’s like this:
lily : / % echo $OLDPWD
lily : / % cd ~
lily : ~ % echo $OLDPWD
/
lily : ~ % cd Desktop
/Users/Liliana Newton/Desktop
lily : ~/Desktop % echo $OLDPWD
/Users/Liliana Newton
lily : ~/Desktop % cd -
/Users/Liliana Newton
lily : ~ % echo $OLDPWD
/Users/Liliana Newton/Desktop
lily : ~ % cd -
/Users/Liliana Newton/Desktop
lily : ~/Desktop % echo $OLDPWD
/Users/Liliana Newton
lily : ~/Desktop %