We characterize the Schauder and unconditional basis properties for Haar system in Triebel–Lizorkin spaces $$F^s_{p,q}({{\mathbb {R}}}^d)$$ , at endpoint cases $$s=1$$ $$s=d/p-d$$ $$p=\infty $$ . Together with earlier results Garrigós et al. (J Fourier Anal Appl 24(5):1319–1339, 2018) Seeger Ullrich (Math Z 285:91–119, 2017), this completes picture such scale, complements a similar study Besov ...