3' RACE reaction gives an artifact generated with kit's anchor primer alone.

[Michael Shapira]

I need help in cDNA cloning:

I am trying to clone the 3' end of a certain cDNA using the Boeringer
5'/3' RACE Kit and I get a product that can be generated with the anchor
primer supplied with the kit alone. I sequenced part of this artifact
product and it contains the sequence of the oligo dT anchor primer used
for first strand cDNA synthesis on both ends.

What could be the reason for this and how can I overcome it?