The assumption for measuring a discrete sample by spinner magnetometer in paleomagnetism is that the sample under study is a magnetic dipole so that the magnetization vector can be calculated by successive measurements of components along three orthogonal axes. This assumption may not hold for samples with inhomogeneous magnetization, irregular shape, or both, where non-dipole components are no longer ignorable. This study draws attention to their effect on the measurement of remanent magnetization based on an offset dipole model using multipole expansion of magnetic potential. Results from this model are compared with the experimental data measured by a new type of spinner magnetometer featured by high spatial resolution and the capability of measuring the fundamental wave component as well as the harmonic wave components. By using the relative amplitude of the harmonic waves to the fundamental wave, the contribution of non-dipole components can be quantified, leading to assessing how dipolar a sample is. The new analyses and instrumentation will be useful as a new diagnostic tool to obtain more reliable data from the samples collected from tectonically active regions with complicated geological histories.