  The J$_1$-J$_2$ Ising model in the square lattice in the presence of an
external field is studied by two approaches: the Cluster Variation Method (CVM)
and Monte Carlo simulations. The use of the CVM in the square approximation
leads to the presence of a new equilibrium phase, not previously reported for
this model: an Ising-nematic phase, which shows orientational order but not
positional order, between the known stripes and disordered phases. Suitable
order parameters are defined and the phase diagram of the model is obtained.
Monte Carlo simulations are in qualitative agreement with the CVM results,
giving support to the presence of the new Ising-nematic phase. Phase diagrams
in the temperature-external field plane are obtained for selected values of the
parameter $\kappa=J_2/|J_1|$ which measures the relative strength of the
competing interactions. From the CVM in the square approximation we obtain a
line of second order transitions between the disordered and nematic phases,
while the nematic-stripes phase transitions are found to be of first order. The
Monte Carlo results suggest a line of second order nematic-disordered phase
transitions in agreement with the CVM results. Regarding the stripes-nematic
transitions, the present Monte Carlo results are not precise enough to reach
definite conclusions about the nature of the transitions.
