  We propose a new way of analyzing, and analytically representing, the
ringdown part of the gravitational wave signal emitted by coalescing black hole
binaries.By contrast with the usual {\it linear} decomposition of the
multipolar complex waveform $h(t)$ in a sum of quasi-normal modes, our
procedure relies on a {\it multiplicative} decomposition of $h(t)$ as the
product of the fundamental quasi-normal mode with a remaining time-dependent
complex factor whose amplitude and phase are separately fitted. As an
illustrative example, we apply our analysis and fitting procedure to the
ringdown part of a sample of sixteen $\ell=m=2$ equal-mass, spinning,
nonprecessing, numerical waveforms computed with the SP$_{\rm E}$C code,now
publicly available in the SXS catalogue. Our approach yields an efficient and
accurate way to represent the ringdown waveform, thereby offering a new way to
complete the analytical effective-one-body inspiral-plus-plunge waveform.
