We present a new data structure for maintaining a set of records in a linear list according to their key values. This data structure has the property that we can keep a number of fingers at points of interest in the key space (e.g., the beginning or the end of the list), so that access and modification in the neighborhood of a finger is very efficient. In the Section 2 we discuss the general structure of our B-tree. Since we propose to search the tree from a leaf upwards, additional links need to be introduced. In Section 3 we show how to obtain our result for the case of one finger. A key idea is the construction of a number representation behaving as described above, which we can use to model the propagation of modifications in the B-tree along the finger path. In Section 4 we generalize the structure so that several fingers in the key space can be maintained, with the advantage that access is cheap in the neighborhood of each finger. Finally in Section 5 we present some implementation notes and applications, mostly to sorting.