  We present a new spectral-method-based algorithm for finding apparent
horizons in three-dimensional space-like hypersurfaces without symmetries.
While there are already a wide variety of algorithms for finding apparent
horizons, our new algorithm does not suffer from the same weakness as previous
spectral apparent horizon finders: namely the monopolar coefficient ($\ell=0$
in terms of the spherical harmonics decomposition) needed to be determined by a
root-finding procedure. Hence, this leads to a much faster and more robust
spectral apparent horizon finder. The finder is tested with the Kerr-Schild and
Brill-Lindquist data. Our finder is accurate and is as efficient as the
currently fastest methods developed recently by Schnetter (2003 Class. Quantum
Grav. {\bf 20}, 4719) and Thornburg (2004 Class. Quantum Grav. {\bf 21}, 743).
At typical resolutions it takes only 0.5 second to find the apparent horizon of
a Kerr-Schild black hole with $a=0.9M$ to the accuracy $\sim 10^{-5}$ for the
fractional error in the horizon's location on a 2 GHz processor.
