Perl is excellent for simple stuff like this. (grin)
You could probably do it like this:
Open the input file, and open an output file. Copy each line from input to output. Keep a line number for each input line; it would be 1 for the first line, 2 for the second, and so on. If an input line contains the pattern of interest, set another variable (let's call it $elephant) equal to the current line number; otherwise, leave $elephant alone. Then, before you output the current line, compare the current line number with $elephant. If it's equal to $elephant, or equal to $elephant+1, don't output this line.
For this to work, you'll need to set $elephant to something like -1 at the beginning; otherwise, the first line will not be output because the line number will be 1 and $elephant will be 0.
If you're not familiar with Perl, http://perldoc.perl.org
is your friend. In particular, I'd recommend you visit:
And when you're ready to eat the whole enchilada:
Hope this helps.