  Ulf Rehmann and Jun Morita, in their 1989 paper "A Matsumoto-type theorem for
Kac-Moody groups", gave a presentation of $K_2(A,F)$ for any generalised Cartan
matrix $A$ and field $F$. The purpose of this paper is to use this presentation
to compute $K_2(A,F)$ more explicitly in the case when $A$ is hyperbolic. In
particular, we shall show that these $K_2(A,F)$ can always be expressed as a
product of quotients of $K_2(F)$ and $K_2(2,F)$. Along the way, we shall also
prove a similar result in the case when $A$ has an odd entry in each column.
