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The predictions of standard Higgs inflation in the framework of the metric formalism yield a tensor-to-scalar ratio r similar to 10(-3) which lies well within the expected accuracy of near-future experiments similar to 10(-4). When the Palatini formalism is employed, the predicted values of r get highly suppressed r similar to 10(-12) and consequently a possible nondetection of primordial tensor fluctuations will rule out only the metric variant of the model. On the other hand, the extremely small values predicted for r by the Palatini approach constitute contact with observations a hopeless task for the foreseeable future. In this work, we propose a way to remedy this issue by extending the action with the inclusion of a generalized nonminimal derivative coupling term between the inflaton and the Einstein tensor of the form m(-2)(phi)G(mu nu)del(mu) phi del(nu)phi. We find that with such a modification, the Palatini predictions can become comparable with the ones obtained in the metric formalism, thus providing ample room for the model to be in contact with observations in the near future.