  We present a new short proof of the explicit formula for the group of links
(and also link maps) in the 'quadruple point free' dimension. Denote by
$L^m_{p,q}$ (respectively, $C^{m-p}_p$) the group of smooth embeddings
$S^p\sqcup S^q\to S^m$ (respectively, $S^p\to S^m$) up to smooth isotopy.
Denote by $LM^m_{p,q}$ the group of link maps $S^p\sqcup S^q\to S^m$ up to link
homotopy.
  Theorem 1. If $p\le q\le m-3$ and $2p+2q\le 3m-6$ then \begin{equation*}
L^m_{p,q}\cong \pi_p(S^{m-q-1})\oplus\pi_{p+q+2-m}(SO/SO_{m-p-1})\oplus
C^{m-p}_p\oplus C^{m-q}_q. \end{equation*} Theorem 2. If $p, q\le m-3$ and
$2p+2q\le 3m-5$ then $LM^m_{p,q}\cong \pi^S_{p+q+1-m}$.
  Our approach is based on the use of the suspension operation for links and
link maps, and suspension theorems for them.
