  We consider the contribution to $K \rightarrow 2 \pi$ decays from the
non-diagonal $s \ra d$ quark transition amplitude. First, we calculate the most
important part of the $s \rightarrow d$ transition, the so-called self-penguin
amplitude $\sim G_F \alpha_s$, including the heavy top-quark case. Second, we
calculate the matrix element of the $s \rightarrow d$ transition for the
physical $K \rightarrow 2 \pi$ process. This part of the analysis is performed
within the Chiral Quark Model where quarks are coupled to the pseudoscalar
mesons. The CP-conserving self-penguin contribution to $K \rightarrow 2\pi$ is
found to be negligible. The obtained contribution to $\epsilon'/\epsilon$ is
sensitive to the values of the quark condensate $<\bar{q} q>$ and the
constituent quark mass $M$. For reasonable values of these quantities we find
that the self-penguin contribution to $\epsilon'/\epsilon$ is 10-15% of the
gluonic penguin contribution and has the same sign. Given the large
cancellation between gluonic and electroweak penguin contributions, this means
that our contribution is of the same order of magnitude as $\epsilon'/\epsilon$
itself.
