  We propose to use a basis function constructed based on the microscopic
cluster model for an efficient description of multi-cluster systems with the
orthogonality condition originating from the Pauli principle. The basis
function is expressed analytically by a superposition of correlated Gaussian
functions. We demonstrate the power of this approach by taking an example of a
$3\alpha$ system, $^{12}$C. A comparison with the conventional pseudopotential
method using the projection operator is made. The present method offers
efficient and numerically stable computations as the number of basis functions
is significantly reduced compared to the conventional method. We show that the
present basis function includes reasonably small components of the
Pauli-forbidden states, allowing us to discuss simply the structure of the
first excited $0^+$ state, Hoyle state.
