A streaming tape drive for use in computer systems for the storage and retrieval of data on magnetic tape has the capability of locating a selected block of data stored on magnetic tape in serpentine fashion by first moving the magnetic head of the tape drive from one data track to another data track until the head is positioned to a data track which has a data block having a block number that is within a predetermined numeric value of the block number of the selected data block for which tape drive is searching. After the head is so moved to the data track, the tape drive performs a sequential search of the tape on a block-by-block basis until the selected data block is found. The tape drive has the capability to perform such searches on magnetic tape that is recorded in standard serpentine fashion, and no special tape recording format is required.