Lets consider that there is a text in the following format:
"this\n is >\n<"
"this\n is ><"
echo "this\n is >\n<" | sed -e 's/>\n<//g'
echo "this\n is >\n<" | sed -e 's/>\\n</></g'
This might work for you (GNU sed):
sed ':a;N;s/>\n</></;ta;P;D' file
Read two lines into the pattern space and if the newline is between
< remove it. Then print and delete the first line and repeat.