  We present an explicit polynomial formula for evaluating the principal
logarithm of all matrices lying on the line segment $\{I(1-t)+At:t\in [0,1]\}$
joining the identity matrix $I$ (at $t=0$) to any real matrix $A$ (at $t=1$)
having no eigenvalues on the closed negative real axis. This extends to the
matrix logarithm the well known Putzer's method for evaluating the matrix
exponential.
