  We provide exact analytical expressions for the magnetic susceptibility
function in the high temperature expansion for finite Heisenberg spin systems
with an arbitrary coupling matrix, arbitrary single-spin quantum number, and
arbitrary number of spins. The results can be used to determine unknown
exchange parameters from zero-field magnetic susceptibility measurements
without diagonalizing the system Hamiltonian. We demonstrate the possibility of
reconstructing the exchange parameters from simulated data for two specific
model systems. We examine the accuracy and stability of the proposed method.
