We investigate the subsequence $\sigma^{T}_{2^n}(f)$ of matrix transform means with respect to the Walsh system generated by nonincreasing and convex sequences $t_{k,n} $ determined by matrix $T$. In particular, we prove for any $0 \lt p \lt 1/(1+\gamma)$ that there exists a martingale $f \in H_{p}(G)$ such that \[ upimits_{nı\mathbb{N}}eft\|igma^{T}_{2^{n}}(f)\right\|_{weak-L_{p}}=ıfty, \] where $\gamma$ depends on the sequences $t_{k,n}.$