  Taylor expansion of the equation of state of QCD suffers from shortcomings at
chemical potentials $\mu_B \geq (2-2.5)T$. First, one faces difficulties
inherent in performing such an expansion with a limited number of coefficients;
second, higher order coefficients determined from lattice calculations suffer
from a poor signal-to-noise ratio. In this work, we present a novel scheme for
extrapolating the equation of state of QCD to finite, real chemical potential
that can extend its reach further than previous methods. We present continuum
extrapolated lattice results for the new expansion coefficients and show the
thermodynamic observables up to $\mu_B/T\le3.5$.
