Summary: Let \(\Omega\) be a smooth bounded domain in \(\mathbb{R}^n\) and denote the regular part of the Green function on \(\Omega\) with Dirichlet boundary condition by \(H(x,y)\). Assume the integer \(k_0\) is sufficiently large, \(q\in \Omega\) and \(n\geq5\). For \(k\geq k_0\) we prove that there exist initial data \(u_0\) and smooth parameter functions \(\zeta (t)\to q\) and \(0< \mu (t)\to 0\) for \(t\to+\infty\) such that the solution \(u_q\) of the critical nonlinear heat equation \[\begin{cases} u_t=\Delta u+ |u|^{\frac{4}{n-2}}u \quad & \text{in }\Omega\times(0,\infty) \\ u=0\quad & \text{on } \partial\Omega\times(0,\infty) \\ u(\cdot,0)=u_0 \quad & \text{in } \Omega \end{cases}\] has the form \[ u_q(x,t)\approx \mu(t)^{-\frac{n-2}{2}}\left(Q_k \left(\frac{x-\zeta(t)}{\mu(t)} \right)-H(x,t) \right), \] where the profile \(Q_k\) is the non-radial sign-changing solution of the Yamabe equation \[ \Delta Q+ |Q|^{\frac{4}{2-n}}Q=0\text{ in }\mathbb{R}^n, \] constructed in [the first author et al., J. Differ. Equations 251, No. 9, 2568–2597 (2011; Zbl 1233.35008)]. In dimension 5 and 6 we also investigate the stability of \(u_q(x,t)\).