Tamper detection and localization are essential things in fragile image watermarking to carry out the authentication process. The tampering method continues to evolve from general and complex tampering. This study proposes a tamper detection and localization technique that can withstand a variety of standard and complex attacks with a combination of bidiagonal singular value decomposition, blockwise and group block for authentication. The least significant bit method is used in the embedding process to increase imperceptibility. By combining these methods, fragile image watermarking is produced that is robust against various common tampers such as type I and type II copypaste, rotate, text addition, and noise addition, as well as various complex attacks such as vector quantization, collage, content only and constant feature. The tamper detection rate is more than 0.99, and the average PSNR value is 51.85 dB. This shows that the proposed method is robust against various tampers and has excellent imperceptibility.