I\'m looking for a line in bash that would work on both linux as well as OS X to remove the second line containing the desired string:
Header 1 2 ... Header 10 1
This might work for you (GNU sed):
sed -i '1b;/^Header/d' file
Ignore the first line and then remove any occurrence of a line beginning with Header.
Header
To remove subsequent occurrences of the first line regardless of the string, use:
sed -ri '1h;1b;G;/^(.*)\n\1$/!P;d' file