Abstract : We show that non-minimal inflation , based on the \phi ^ { 4 } potential , may be rendered unitarity conserving and compatible with the Planck results for 4.6 \cdot 10 ^ { -3 } \leq r _ { 21 } = c _ { 2 \cal R } / c _ { 1 \cal R } ^ { 2 } \leq 1 , if we introduce a linear contribution ( c _ { 1 \cal R } \phi ) to the frame function which takes the form f _ { \cal R } = 1 + c _ { 1 \cal R } \phi + c _ { 2 \cal R } \phi ^ { 2 } . Supersymmetrization of this model can be achieved by considering two gauge singlet superfields and combining a linear-quadratic superpotential term with a class of logarithmic or semi-logarithmic Kähler potentials with prefactor for the logarithms including the inflaton field - ( 2 n + 3 ) or -2 ( n + 1 ) where -0.01 \lesssim n \lesssim 0.013 . PACs numbers : 98.80.Cq , 04.50.Kd , 04.65.+e Published in Phys . Lett B 789 , 243 ( 2019 )