  We present an explicit description of all harmonic maps of finite uniton
number from a Riemann surface into a complex Grassmannian. Namely, starting
from a constant map $Q$ and a collection of meromorphic functions and their
derivatives, we show how to algebraically construct all harmonic maps from the
two-sphere into a given Grassmannian $G_p(\mathbb C^n)$. In this setting the
uniton number depends on $Q$ and $p$ and we obtain a sharp estimate for it.
