awk to start with symbol and print next

File A

>answer is the predicted other than >bigger than two
>whatever isthere >out of mind
CGAHHAWWASSASS
SASAWEDSASSDDD
SSDDDEDEUJUYYS
>hello you are there other is what is that>you are not
serious>leave it
SSSAAAAAASS
ASWWQQDDD
WESEEWWWW
WEEEEEWSS
SJUJSGKKSSS
SWBVHJJWUW
>hi i am coming to that place >if you are not
there >something interesting
ASJSUWGJNDGSDBSSKKS
SSGWBSGGSJSKKLLSSJS
SHHHSYWJJKJKKSSK
KAIJWGBSKJJSJJJJJJSOWB

And the output should be
>answer is the predicted other than
CGAHHAWWASSASS
SASAWEDSASSDDD
SSDDDEDEUJUYYS
>hello you are there other is what is that
SSSAAAAAASS
ASWWQQDDD
WESEEWWWW
WEEEEEWSS
SJUJSGKKSSS
SWBVHJJWUW
>hi i am coming to that place
ASJSUWGJNDGSDBSSKKS
SSGWBSGGSJSKKLLSSJS
SHHHSYWJJKJKKSSK
KAIJWGBSKJJSJJJJJJSOWB

So If the first line in each red clor start with symbol > then another same symbol (>)came then it should not print but the next blue line (blue colour)

how can the awk or anything else command can work out..

try this "untested" :

awk '/^>/{print;getline};!/>/' file

actually same output will print
while running this awk code but second line have been removed but not still
>answer is the predicted other than >bigger than two
CGAHHAWWASSASS
SASAWEDSASSDDD
SSDDDEDEUJUYYS
>hello you are there other is what is that>you are not
SSSAAAAAASS
ASWWQQDDD
WESEEWWWW
WEEEEEWSS
SJUJSGKKSSS
SWBVHJJWUW
>hi i am coming to that place >if you are not
ASJSUWGJNDGSDBSSKKS
SSGWBSGGSJSKKLLSSJS
SHHHSYWJJKJKKSSK
KAIJWGBSKJJSJJJJJJSOWB

Hi,

try:

awk 'f==0 && /^>/{sub(/>[^>]*$/,"",$0);print $0;f=1}!/.*>.*/{print $0;f=0}' file

It gives me:

>answer is the predicted other than 
CGAHHAWWASSASS
SASAWEDSASSDDD
SSDDDEDEUJUYYS
>hello you are there other is what is that
SSSAAAAAASS
ASWWQQDDD
WESEEWWWW
WEEEEEWSS
SJUJSGKKSSS
SWBVHJJWUW
>hi i am coming to that place 
ASJSUWGJNDGSDBSSKKS
SSGWBSGGSJSKKLLSSJS
SHHHSYWJJKJKKSSK
KAIJWGBSKJJSJJJJJJSOWB