  A well-known theorem of Mathieu's states that a Harish-chandra module over
the Virasoro algebra is either a highest weight module, a lowest weight module
or a module of the intermediate series. It is proved in this paper that an
analogous result also holds for the Lie algebra $\BB$ related to Block type,
with basis {L_{\a,i},C|a,i\in\Z, i\ge0} and relations
[L_{\a,i},L_{\b,j}]=((i+1)\b-(j+1)\a)L_{\a+\b,i+j}+\d_{\a+\b,0}\d_{i+j,0}\frac{\a^3-\a}{6}C,
[C,L_{\a,i}]=0.Namely, an irreducible quasifinite $\BB$-module is either a
highest weight module, a lowest weight module or a module of the intermediate
series.
