A method for manufacturing a membrane assembly for lithography, the method comprising: providing a stack comprising a membrane layer between a supporting substrate and an attachment substrate, wherein the supporting substrate comprises a first inner region and a first border region and wherein the attachment substrate comprises a second inner region and a second border region; processing the stack, including selectively removing the first inner region of the supporting substrate and selectively removing the second inner region of the attachment substrate, to form a membrane assembly comprising: a membrane formed from at least the membrane layer, and a support holding the membrane, the support being formed partially from the first border region of the supporting substrate and partially from the second border region of the attachment substrate; characterized, in that the membrane assembly formed is a pellicle for EUV lithography; in that the supporting substrate further comprises a first edge region around the first border region; in that the attachment substrate further comprises a second edge region around the second border region, and in that the step of processing the stack further includes: - separating the first edge region, and layers formed on the first edge region, from the stack before selectively removing the first inner region of the supporting substrate, and - separating the second edge region, and layers formed on the second edge region, from the stack before removing the second inner region of the attachment substrate. providing a stack comprising a membrane layer between a supporting substrate and an attachment substrate, wherein the supporting substrate comprises a first inner region and a first border region and wherein the attachment substrate comprises a second inner region and a second border region; processing the stack, including selectively removing the first inner region of the supporting substrate and selectively removing the second inner region of the attachment substrate, to form a membrane assembly comprising: a membrane formed from at least the membrane layer, and a support holding the membrane, the support being formed partially from the first border region of the supporting substrate and partially from the second border region of the attachment substrate; a membrane formed from at least the membrane layer, and a support holding the membrane, the support being formed partially from the first border region of the supporting substrate and partially from the second border region of the attachment substrate; in that the membrane assembly formed is a pellicle for EUV lithography; in that the supporting substrate further comprises a first edge region around the first border region; in that the attachment substrate further comprises a second edge region around the second border region, and in that the step of processing the stack further includes: - separating the first edge region, and layers formed on the first edge region, from the stack before selectively removing the first inner region of the supporting substrate, and - separating the second edge region, and layers formed on the second edge region, from the stack before removing the second inner region of the attachment substrate. - separating the first edge region, and layers formed on the first edge region, from the stack before selectively removing the first inner region of the supporting substrate, and - separating the second edge region, and layers formed on the second edge region, from the stack before removing the second inner region of the attachment substrate.