if string is there then do nothing

I am trying to create an if statement that searches for the string and if its there don't do anything my script is still writing into the file I want it to not write if the string is there and if its not there then write the string into the file this is what I have.


if grep -q "string" /etc/syslog.conf
then
sed -i -e '/^authpriv.info/ a\
authpriv.none\t\t\t\t\t\t\t/var/log/secure' /etc/syslog.conf
else
     if grep -q "string" /etc/syslog.conf
     then
     echo "authprive.none exists"

     fi
fi