Abstract. In this paper, we study a class of spacelike rotational surfacesin the Minkowski 4-space E 41 with meridian curves lying in 2-dimensionalspacelike planes and having pointwise 1-type Gauss map. We obtain allsuch surfaces with pointwise 1-type Gauss map of the first kind. Thenwe prove that the spacelike rotational surface with flat normal bundleand pointwise 1-type Gauss map of the second kind is an open part of aspacelike 2-plane in E 41 . 1. IntroductionThe notion of finite type submanifolds of Euclidean spaces was introducedby B.-Y. Chen in late 1970’s [2]. Since then many works have been done tocharacterize or classify submanifolds of Euclidean space or pseudo-Euclideanspace in terms of finite type. Also, B.-Y. Chen and P. Piccinni extended thenotion of finite type to differentiable maps, in particular, to Gauss map ofsubmanifolds in [4]. A smooth map φ on a submanifold M of a Euclidean spaceor a pseudo-Euclidean space is said to be of finite type if φ can be expressed as afinite sum of eigenfunctions of the Laplacian ∆ of M, that is, φ = φ