  We have developed a matrix model for FQH states at filling factor
\nu_{k_1k_2} going beyond the Laughlin theory. To illustrate our idea, we have
considered an FQH system of a finite number N=(N_{1}+N_{2}) of electrons with
filling factor \nu_{k_{1}k_{2}} = \nu_{p_{1}p_{2}}=\frac{p_{2}}{p_{1}p_{2}-1};
p_{1} is an odd integer and p_{2} is an even integer. The \nu_{p_{1}p_{2}}
series corresponds just to the level two of the Haldane hierarchy; it recovers
the Laughlin series \nu_{p_{1}} =\frac{1}{p_{1}} by going to the limit p_{2}
large and contains several observable FQH states such as \nu = 2/3, 2/5, >....
