  Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if
$\square_\lambda$ holds, then this may be witnessed by a coherent sequence $<
C_\alpha | \alpha < \lambda^+ >$ with the following remarkable guessing
property:
  For every sequence $< A_i | i<\lambda >$ of unbounded subsets of $\lambda^+$,
and every limit $\theta<\lambda$, there exists some $\alpha<\lambda^+$ such
that $\otp(C_\alpha)=\theta$, and the $(i+1)_{th}$-element of $C_\alpha$ is a
member of $A_i$, for all $i<\theta$.
  As an application, we construct an homogenous $\lambda^+$-Souslin tree from
$GCH+\square_\lambda$, for every singular cardinal $\lambda$.
  In addition, as a by-product, a theorem of Farah and Velickovic, and a
theorem of Abraham, Shelah and Solovay are generalized to cover the case of
successors of regulars.
