Off topic:how to convert a big fasta file into several smaller one

Question

[yaqinguo629]

Hi, everyone. I have a big fasta file as below:
>OTU1
ATCGAATTCGATCGAATTCG
>OTU2
TTCGAATTCGCCATATCGAATTCG
...
>OTU800
ATCGAATTCGATCGAATTCGATCGAATTCG
I want to put each sequence into the fasta file, like this:
OTU1.fasta
OTU2.fasta
...
OTU800.fasta
Can anyone help me with this? I prefer to use AWK script. Thanks in advance!