cat and grep without destroying file

[(=?utf-8?q?=60=60-=5F-=C2=B4=C2=B4?=) -- Fernando]

I've been trying to make a small shell script that would remove a line from a text file.
But every time that I pipe the content of grep to the original file, the file ends up blank.
So, I've made the script use a copy and them replace the original.
It looks like this:
#for i in $(/bin/ls -1); do cat $i | egrep -v ^Date > $i.new; mv $i.new $i; done

Isn't there any other way, without using the mv?

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