  Given smooth manifolds $V^n$ and $M^m$, an integer $k$, and an immersion
$f:V\looparrowright M$, we have constructed an obstruction for existence of
regular homotopy of $f$ to an immersion $f':V\looparrowright M$ without
$k$-fold points. This obstruction takes values in certain framed bordism group,
and for $(k+1)(n+1)\leq km$ turns out to be complete.
