Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ-r of unknown parameter λ of gamma distribution with density $$f\left( {x|\lambda , b} \right) = \lambda ^{b - 1} e^{\lambda x} x^{b - 1} /\Gamma \left( b \right)$$ ,x> 0, whereb-known parameter, for loss function $$L(\hat \lambda ^{ - r} ,\lambda ^{ - r} ) = (\hat \lambda ^{ - r} - \lambda ^{ - r} )^2 /\lambda ^{2r} $$ . Goodmann in [1] choosing three loss functions of different shape found unbiased Lehmann-estimators, of the variance σ2 of the normal distribution. In particular for quadratic loss function he took weight of the formK(σ2)=C andK(σ2)=(σ2)-2 only. In this work we obtained the class of all unbiased Lehmanns-estimators of the variance λ2 of the exponential distribution, among estimators of the form $$\alpha (n)(\mathop \sum \limits_l^n X_i )^2 - ie$$ functions of the sufficient statistics-with quadratic loss function with weight of the form $$K(\lambda ^2 ) = C(\lambda ^2 )^{C_1 } $$ ,C>0.