  We propose a protocol to improve the accuracy of direct complex state
measurements (DSM) by using rebits in real Hilbert spaces. We show that to
improve the accuracy, the initial complex state should be decomposed into the
real and imaginary parts and stored in an extended state (rebit) which can be
tracked individually by two bases of an extra qubit. For pure states, the
numerical calculations show that the trace distances between the true state and
the reconstructed state obtained from the rebit method are more precise than
those ones obtained from the usual DSM and quantum state tomography (SQT)
because the number of projective measurements is reduced. For mixed states, the
rebit method gives the same accuracy in comparison to the usual DSM, while it
is less precise than QST. Its precision is also significantly improved when
using nearly-pure states. Our proposal holds promises as a reliable tool for
quantum computation, testing of quantum circuits by using only real amplitudes.
