  We determine all cases for which the $d$-dimensional Haar wavelet system
$H^d$ on the unit cube $I^d$ is a conditional or unconditional Schauder basis
in the classical isotropic Besov function spaces ${B}_{p,q,1}^s(I^d)$,
$0<p,q<\infty$, $0\le s < 1/p$, defined in terms of first-order $L_p$ moduli of
smoothness. We obtain similar results for the tensor-product Haar system
$\tilde{H}^d$, and characterize the parameter range for which the dual of
${B}_{p,q,1}^s(I^d)$ is trivial for $0<p<1$.
