Sample file:

This is line one,
this is another line,
this is the PRIMARY INDEX line
l ;
This is another line

This is line one,
this is another line
this is the PRIMARY INDEX line
;
This is another line

Try something like this:

awk '/PRIMARY INDEX/{sub(/.$/,x,p);print p RS $0;getline;sub(/^./,z);print;next}p{print p}{p=$0}' infile

Thank you for your quick respose. It almost works.
The only problem is it replaces the last line with the line before the matching line at the end. The two lines "this is another line" in my previous sample are not always the same (I should have used different lines).
For example if the sample file is:

This is line one,
this is another line
this is the PRIMARY INDEX line
 ;
this is yet a different line

This is line one,
this is another line
this is the PRIMARY INDEX line
 ;
this is another line

Could you please explain the logic?

Thanks.

Like this?

awk '/PRIMARY INDEX/{sub(/.$/,x,p);print p RS $0;if(getline){sub(/^./,x);print}p=x;next}
     p{print p}{p=$0}END{if(p)print p}' infile

This worked perfectly. Thank you very much for your help.