We propose a non-Hermitian generalization of stimulated Raman adiabatic passage (STIRAP), which allows one to increase speed and fidelity of the adiabatic passage. This is done by adding balanced imaginary (gain/loss) terms in the diagonal (bare energy) terms of the Hamiltonian and choosing them such that they cancel exactly the nonadiabatic couplings, providing in this way an effective shortcut to adiabaticity. Remarkably, for a STIRAP using delayed Gaussian-shaped pulses in the counter-intuitive scheme the imaginary terms of the Hamiltonian turn out to be time independent. A possible physical realization of non-Hermitian STIRAP, based on light transfer in three evanescently-coupled optical waveguides, is proposed. ; Comment: 7 pages, 4 figures